Cheat sheet · Money & Banking

Two columns, no chrome, one section per half. Ctrl+P (Windows) / ⌘P (Mac).

Money & Banking · Pre mid-sem

Definitions to write verbatim

Financial system — a framework which facilitates efficient flow of funds from saving to investment by bringing savers and borrowers together via financial markets and financial institutions.
Private saving — the portion of households' income not used for consumption or paying taxes. Public saving = T − G. National saving = private + public.
Financial deepening and financial broadening, always as a pair. Market-based versus bank-based financial system design.
Banks are creators and purveyors of credit; non-banks are purveyors of credit only. Depository versus non-depository institutions. Surplus units and deficit units.
Financial mediation — direct, through the capital market, versus indirect, through institutions such as banks. Note the professor says mediation, not intermediation.
Money market — maturity up to one year, close substitutes for money, liquid, turned over quickly at low cost.
T-Bills — issued by the RBI on behalf of the Central Government, risk-free and highly liquid, sold by auction, issued at a discount to their true (PAR) value, no coupon. Only the Centre issues them.
Repo — sell now, agree to buy back later, so borrowing for the seller. Reverse repo — the same trade from the lender's side.
Securitisation — converting illiquid assets into tradable securities: a homogeneous pool of loans with predictable future cash flows transferred from the originator to a special purpose vehicle (SPV/SPE), repackaged into securities, with the assets legally isolated.
Clean price, dirty (invoice) price, accrued interest. Yield to maturity — the single discount rate that makes the present value of the bond's cash flows equal its current price.
Hybrid financing — instruments with characteristics of both debt and equity, "where debt and equity meet in the middle". Preference capital is the main source.

Saving, investment and interest rates

Private saving = Y - T - C Public saving = T - G National saving = Y - C - G Budget deficit = G - T
Y = C + I + G + NX (closed: Y = C + I + G, so I = national saving)
Fisher, approximate: ir = i - pi_e Fisher, exact: (1 + N) = (1 + R)(1 + I)
Class exercise, worked: GDP $10 trn, C $6.5 trn, G $2 trn, deficit $300 bn. Public saving −0.3, taxes 1.7, private saving 1.8, national saving 1.5, investment 1.5.
Loanable funds theory. Demand shifters: wealth, expected returns, risk of bonds relative to alternatives, liquidity. Supply shifters: expected profitability of investment, expected inflation, government deficit.
Eight factors affecting interest rates: demand and supply of money, inflation, monetary policy, credit risk, loan term, economic conditions, government policies, global factors.
Trap: the exact Fisher form and the approximation differ. At R = 3% and I = 5%, exact N = 8.15%, approximation 8%. State which you used.

Money market arithmetic

T-bill price = par / (1 + r x n/365) One-year bill: price = par / (1 + r)
Yield = ((SP - PP) / PP) x (365 / n) Indian form: Y = ((100 - P)/P) x (365/D) x 100
Worked: ₹10,000 par, 7% required, one year → price ₹9,345.79. Bill at ₹98 redeeming ₹100 over 91 days → yield 8.19%. Price 98.20 on a 91-day bill → yield 7.35%.
Section B only: a 90-day T-bill, face 100, ask discount 4.9% → discount = 100 × 4.9/100 × 90/360 = 1.225, so price 98.775. Note the 360-day convention here against 365 elsewhere.
Ladder: call money overnight · notice money 2 to 14 days · term money 15 days to 1 year. CDs 7 days to 1 year, minimum ₹1 lakh, demat or usance promissory note.
Trap: 365 or 360 days? Read the question. And a discount quoted on face value is not the same as a yield quoted on price.

Bond arithmetic

P = SUM [ C / (1+r)^t ] + F / (1+r)^n = C x PVIFA(r,n) + F x PVIF(r,n)
HPR = (price gain or loss + coupon received) / purchase price Current yield = annual coupon / current market price YTM (approx) = [C + (prem or disc / years)] / [(P0 + F) / 2]
Dirty price = clean price + accrued interest Accrued interest = coupon x (days since last coupon / days between coupons) ERR = current yield + capital gain yield
Worked: buy at ₹900, ₹100 coupon, sell at ₹1,000 → HPR 22.22%; sell at ₹750 → −5.55%. Four-year 7% bond, face ₹1,000, price ₹905 → YTM 9.8%. Four-year $100 bond, 5% coupon, 4% required → price $103.63.
Section B only, Prof. Panda: 30-year 10% bond, $100 face, 5% YTM → P0 = 176.86, price just before the first coupon 185.71, just after 175.71. That is the saw-tooth and pull to par.
Section B only: between coupon dates, ACT/ACT. T-bond valued 15 Aug 2024: P1− = 1,230.17, K = 77/184 = 0.4186, dirty 1,205.30, AI 34.884, clean 1,170.42. Excel: PRICE(settlement, maturity, rate, yld, redemption, frequency, [basis]), basis 0 = 30/360, 1 = ACT/ACT.
Six bond risks: interest rate, credit or default, reinvestment, inflation, marketability or liquidity, call risk. A stated YTM is realised only if held to maturity and every coupon is reinvested at the YTM.
Eight classification factors: issuer, security, seniority, credit rating, interest rate, maturity, listing, convertibility. Indian par values ₹1,000, ₹2,000, ₹5,000.

Equity market and the primary market

Private equity — owners cannot sell shares to the public. Two reasons to go public: financing growth, cashing out. Two effects: ownership structure (more owners), capital structure (more equity).
VC — money from wealthy investors and pension funds, locked 5 to 10 years. PE — institutional money, heavy leverage, buy-improve-exit.
Issue types: public issue, IPO, OFS, rights issue (existing shareholders, discounted price, in proportion to holding), private placement, preferential allotment.
Preference share types: cumulative / non-cumulative, participating / non-participating, convertible / non-convertible, redeemable / irredeemable.
Rights: Px = (S0 x P0 + s x Ps) / (S0 + s) R = P0 - Px and Ps + N x R = Px
Section B only, ABCD Industries: 900,000 shares at ₹130, ₹22.5 m at ₹75 → 300,000 new shares, 3 rights each, Px ₹116.25, R ₹13.75. Holder of 3 shares: exercise → ₹390, sell rights → ₹390, do nothing → ₹348.75.
Section B only, the Indian IPO: pre-filing (BRLMs, DRHP), approval (SEBI Observation Letter, RHP with the RoC and a 20% price band, roadshows to QIBs), offering (anchor investor a day early, three days of bidding under ASBA, book building to a cut-off price, allotment, unblocking, demat credit, listing). "Red herring" from the diagonal red-ink disclaimer.
Fama's EMH: weak (past prices), semi-strong (all public information), strong (all information). Index types: price-weighted, value or market-cap-weighted, equal-weighted.

Traps that cost marks

A budget deficit and negative public saving are the same number with opposite signs. Do not double-count.
T-bill yield divides by the purchase price, not by 100 or by par, unless the question uses the professor's Indian form which divides by P.
For YTM by the approximation, the denominator is the average of purchase price and face value, (P0 + F)/2, not the face value.
Current yield is not the coupon rate: the coupon rate divides by face value, current yield by the market price.
In a rights issue the value of a right equals the cum-rights to ex-rights price drop, so R = P0 − Px is the check on your Px.
Show every line. A correct number with no method scores half.

Formula cards

Private saving

Private saving = Y - T - C

When the question gives income, taxes and consumption. If it gives a deficit or surplus instead of taxes, get T out of that first.

Y: National income or GDP for the period
T: Tax revenue collected by the government
C: Household consumption spending

Public saving, surplus and deficit

Public saving = T - G Budget surplus = T - G Budget deficit = G - T = -(public saving)

Whenever the question mentions a surplus or a deficit. Convert it to public saving with the correct sign before using it anywhere else.

T: Tax revenue
G: Government purchases of goods and services

National saving

National saving = private + public = (Y - T - C) + (T - G) = Y - C - G

The short form Y − C − G is fastest, and it never needs taxes. Use the long form as the cross-check.

Y: National income or GDP
C: Household consumption
G: Government purchases

National income accounting identity

Y = C + I + G + NX Closed economy: Y = C + I + G, so I = Y - C - G Open economy: I = Y - C - G - NX

Read the question for the word closed. If the economy is open or NX is given, the closed-economy shortcut is wrong.

I: Investment, that is, spending on new capital
NX: Net exports: exports minus imports, negative for a trade deficit

Financial deepening ratio

Deepening = Credit to the private sector / GDP x 100

When the question asks how deep or developed a system is. It is a stock over a flow, so only comparisons mean anything: this year against last, or one country against another.

Credit: Outstanding credit to the commercial or private sector
GDP: One year's output, at current prices

Market-based share of external financing

Market share = (Bonds + Equity raised) / (Bank credit + Bonds + Equity) x 100 Bank share = Bank credit / total x 100

When asked whether a system is market-based or bank-based. Bonds count on the market side, which is where most marks are dropped.

Bonds: Funds raised through debt securities in the market
Equity raised: Fresh equity raised in the primary market
Bank credit: Loans and advances from banks

Real interest rate, linear form

ir = i - pi(e)

Quick conversions, and whenever the Drive slides or the exercise on slide 13 are the reference. Good enough when both rates are small.

ir: Real interest rate, in per cent
i: Nominal interest rate, the rate actually quoted
pi(e): Expected inflation rate over the same period

Fisher effect, exact form

(1 + N) = (1 + R)(1 + I) N = (1 + R)(1 + I) - 1 R = (1 + N) / (1 + I) - 1

The professor's own statement, and the one to use when either rate is large. The gap against the linear form is always the cross term R x I.

N: Nominal interest rate, as a decimal
R: Real interest rate, as a decimal
I: Inflation rate, as a decimal

Error in the linear approximation

Error (percentage points) = R x I x 100

To decide in one second whether the shortcut is safe. At 3% and 5% the error is 0.15 points; at 10% and 20% it is 2 points.

R: Real rate as a decimal
I: Inflation rate as a decimal

T-bill yield (general form)

YT = ((SP - PP) / PP) x (365 / n)

Any bill bought at one price and sold or redeemed at another. n is the days you held it, not the bill's original tenor.

SP: Selling price, or par value if held to maturity
PP: Purchase price, the money actually invested
n: Number of days held

T-bill yield (Indian percentage form)

Y = ((100 - P) / P) x (365 / D) x 100

The professor's own form, for a bill quoted per 100 of face value and held to maturity. Answer comes out directly in per cent.

P: Discounted price at which the security is purchased
D: Tenure of the bill in days

T-bill price

Price = par / (1 + r x n/365) One-year bill: Price = par / (1 + r)

When the required return is given and the price is asked. The value of a T-bill is the present value of the par value.

r: Investor's required annualised return, as a decimal
n: Days to maturity

Ask discount to price and yield (360-day basis)

Discount = Face x d x n/360 Price = Face - Discount Yield = (Discount / Price) x (360/n) x 100

Section B's numerical, and any question quoting a bill on a discount basis. Note the 360-day year and that the discount rate uses face value while the yield uses price.

d: Quoted ask discount rate, as a decimal
n: Days to maturity
Face: Face value, usually 100

Repo margin and repurchase price

Number of bonds = Cash lent / Repo value per bond (round up) Margin = (Number of bonds x Market value) - Cash lent Repurchase price = Repo value x (1 + repo rate x n/360)

Any repo problem giving both a market value and an agreed repo value. Interest accrues on the repo value; the margin comes from the market value.

Repo value: Agreed value of the collateral for repo purposes, per unit of face
Market value: Traded price of the collateral, per unit of face
n: Repo period in days

Loan-to-value ratio

LTV = Loan amount / Property value x 100 Loan = LTV x Property value Borrower's margin = Property value - Loan

Any mortgage sizing question. The LTV cap decides the loan; the remainder is the borrower's own contribution.

Loan amount: Sanctioned principal
Property value: Value of the collateral as assessed by the lender

Origination fee

Fee = fee rate x Loan amount

Whenever an origination fee is quoted. It applies to the loan, not to the property value.

fee rate: Quoted origination fee, usually a fraction of a per cent
Loan amount: Sanctioned principal, after the LTV cap

Tranche loss waterfall

Loss to a tranche = min(remaining loss, tranche size) Remaining loss passes up to the next tranche Senior tranche is safe until loss > total subordination

Allocating losses in a securitisation or CDO. Always work from the bottom slice upward, and compute total subordination to find the senior tranche's cushion.

tranche size: Face value of that slice of the securities
subordination: Total size of all slices below the one you are pricing

Leverage and the wipe-out point

Leverage L = Assets / Equity Critical asset fall = 1 / L Remaining equity = Equity - (fall % x Assets)

Any leveraged vehicle: an SIV, a margin position, a bank. At 10 to 15 times leverage a fall of 6.7% to 10% erases the equity.

Assets: Market value of what the vehicle holds
Equity: Own funds, the residual after debt

TED spread

TED spread = Interbank rate - Treasury bill yield (same tenor) 1 percentage point = 100 basis points

To measure credit risk in the banking system. Read both legs: a widening spread usually means interbank rates rising and bill yields falling as money runs to safety.

Interbank rate: Rate at which banks lend to each other, at the chosen tenor
Treasury bill yield: Government bill yield at the same tenor

Current yield

Current yield = Annual coupon payment / Current market price x 100

When you want the cash return at today's price. It ignores the pull back to par, so it is not comparable across premium and discount bonds.

Annual coupon payment: Coupon rate x par value, in rupees
Current market price: Traded price, which may be above or below par

Premium, par and discount rule

YTM > Coupon rate -> discount (price < par) YTM = Coupon rate -> par YTM < Coupon rate -> premium (price > par)

To place a bond without doing any present-value arithmetic. Works in both directions: from price to yield, or from yield to price.

YTM: Yield to maturity, the market's required return
Coupon rate: Contractual rate on par value

Clean and dirty price

Dirty (invoice) price = Clean price + Accrued interest Clean price = Dirty price - Accrued interest

Any trade between coupon dates. Quotes are clean; the money that changes hands is dirty.

Accrued interest: Coupon earned by the seller since the last coupon date but not yet paid

Capital indexed bond

Indexed principal = Par x (1 + index rate)^n Coupon paid = Fixed coupon rate x Indexed principal

Prof. Panda's sixth bond type. The rate is fixed, the principal moves, so both the coupon and the redemption amount rise with inflation.

index rate: Annual movement of the inflation index
n: Number of years the principal has been indexed

Bond price (present value)

P = C/(1+r) + C/(1+r)^2 + ... + C/(1+r)^n + F/(1+r)^n

The definition. Use it when there are few periods, or when no factor tables are given. Remember the last period carries both the coupon and the face value.

C: Coupon per period, in rupees: coupon rate x face value / periods per year
r: Required return per period
n: Number of periods to maturity
F: Face or par value

Bond price (factor form)

P = C x PVIFA(r, n) + FV x PVIF(r, n) Semi-annual: halve C, halve r, double n

Prof. Panda's form. Two multiplications instead of n divisions, and the only practical way to price a 20- or 40-period bond by hand.

PVIFA(r,n): Present value interest factor of an annuity, for the coupon stream
PVIF(r,n): Present value interest factor for a single sum, for the face value

Holding period return

HPR = (Price gain or loss + Coupon received) / Price at the beginning

Whenever a bond is bought and then sold rather than held to maturity. Keep the sign on the price change, and remember it is not annualised.

Price gain or loss: Selling price minus purchase price, negative if it fell
Coupon received: Coupons collected during the holding period

Current yield and capital gain yield

Current yield CuY = C / P0 Capital gain yield CGY = (P1 - P0) / P0 Expected return ERR = CuY + CGY

Splitting a one-period return into cash and price components. For a bond held one period the sum equals the YTM per period.

C: Coupon for the period
P0: Price at the start of the period
P1: Price at the end of the period

YTM approximation

YTM = [C + (P or D / years to maturity)] / [(P0 + F) / 2] P or D = F - P0 (positive for a discount, negative for a premium)

Whenever a YTM is asked for by hand. Keep the sign on the premium or discount; forgetting it on a premium bond is the standard error.

C: Annual coupon in rupees
P0: Current market price
F: Face value

Clean, dirty and accrued interest

AI = Coupon x (days since last coupon) / (days between coupons) Dirty (invoice) price = Clean price + AI Clean price = Dirty price - AI

Any trade between coupon dates. Quotes are clean; settlement is dirty.

AI: Accrued interest owed to the seller

Valuation between coupon dates (ACT/ACT)

K = N1 / N2 Dirty price = P1(minus) x PVIF(r, K) AI = Coupon x (1 - K) Clean price = Dirty price - AI

When the settlement date falls between two coupon dates. Price to the next coupon date first, then discount back by the fraction K of one period.

N1: Actual days from today to the next coupon date
N2: Actual days between the two coupon dates
P1(minus): Price as of the next coupon date, just before the coupon is paid

Zero-coupon bond price

P = F / (1 + r)^n

Zero-coupon or deep discount bonds, and each leg of a STRIPS. One cash flow, so one division, and no reinvestment risk.

F: Face value received at maturity
r: Yield per period
n: Number of periods

Rights per new share

N = S0 / s where s = Amount to be raised / Subscription price

The first step of every rights problem. Get s from the money to be raised and the subscription price, never from the market price.

S0: Number of shares outstanding before the issue
s: Number of new shares issued
N: Rights required to buy one new share; need not be a whole number

After-rights price

Px = (S0 x P0 + s x Ps) / (S0 + s)

The ex-rights or theoretical after-rights price. It is a weighted average of the old market price and the subscription price, weighted by share counts.

P0: Cum-rights market price, before the rights go ex
Ps: Subscription price of the new shares
Px: After-rights (ex-rights) price

Value of one right

Ps + N x R = Px -> R = (Px - Ps) / N Identity: P0 = Px + R

To value a right, and to check any rights calculation. The value of a right always equals the fall in the share price from cum-rights to ex-rights.

R: Value of one right
N: Rights needed per new share

Shareholder wealth under the three options

Exercise: (holding + new shares) x Px - (new shares x Ps) Sell rights: holding x Px + rights held x R Do nothing: holding x Px

To show that a rights issue is wealth-neutral. The first two give the same answer as holding x P0; only the third is lower, by exactly the value of the lapsed rights.

holding: Shares owned before the issue
rights held: One per existing share

Price-weighted index

Index = SUM(prices) / divisor New divisor after a corporate action = new price sum / index level to be preserved

When the question gives only prices. The divisor starts as the number of stocks and must be re-solved after any split or constituent change.

prices: Market price of each constituent
divisor: Initially the number of stocks; adjusted to keep the index continuous

Value-weighted index

Index = (SUM(price x shares) / base market cap) x base index value Shortcut: New index = Old index x (new aggregate cap / old aggregate cap)

The method the Sensex and Nifty use. Needs share counts as well as prices, and requires no adjustment for splits.

price x shares: Market capitalisation of each constituent
base market cap: Aggregate capitalisation on the base date
base index value: Index level assigned to the base date, e.g. 100 or 1,000

Equal-weighted index return

Return = (SUM of individual percentage returns) / number of stocks

When every constituent is to count the same. It over-weights small companies relative to the market and needs periodic rebalancing.

individual return: (new price - old price) / old price, per stock

Money & Banking · Post mid-sem

Definitions to write verbatim

Derivative — a financial security whose value is derived from an underlying asset or group of assets.
Forward contract — an obligation to buy or sell a certain asset at a specified price (the forward price) at a specified time, typically not traded on exchanges. Both parties are obligated.
Futures — the same as forwards except settled daily and typically traded on a standardised exchange.
Option — a contract giving the purchaser the right to buy or sell the underlying at a specified price (the strike or exercise price) within a specific period. The writer is obligated if the owner exercises.
Long on option — right and no obligation, loss limited to the premium, profit depends on the underlying. Short on option — obligation and no right, maximum profit the premium, loss theoretically unlimited.
Direct quotation — cost of one unit of foreign currency in local currency. Indirect quotation — cost of one unit of local currency in foreign currency. Base and quote currency.
Law of one price — the price of an identical good will be the same throughout the world. PPP — exchange rates adjust to reflect changes in price levels; works in the long run, not the short run.
Monetary policy — an economic policy that manages the size and growth rate of the money supply. Objectives: inflation and unemployment.
Scheduled commercial bank — fulfils the conditions of the Second Schedule of the Banking Regulation Act, 1949: capital and reserves of at least ₹5 lakh, carrying on banking in India, a corporation or cooperative society and not a partnership or sole proprietorship.
Credit creation — a bank does not provide cash to the borrower; it opens a deposit account from which the borrower can withdraw, so sanctioning a loan automatically creates deposits.
Non-performing asset — an asset ceases to generate income for the bank on an actual realisation basis. Operationally, interest or principal overdue for 90 days.
Mutual fund — an investment company that pools shareholders' money and invests in stocks, bonds or money market securities under professional management, each investor sharing proportionately in income, gains, losses, brokerage and fees. In India a trust under the Indian Trusts Act, 1882.

Derivatives arithmetic

Contract value = lots x lot size x price Long forward profit per unit = S(T) - F(0,T) Short forward profit per unit = F(0,T) - S(T) Default exposure at t = PV{ |F(0,T) - F(t,T)| }
Initial margin = margin % x contract value MTM (short) = (yesterday - today) x quantity Equity = previous equity + MTM + variation margin Call when equity < maintenance; variation = initial - equity
Worked: sell ¥20 m forward at $0.0090, spot $0.0083 → short profits $14,000. Buy 100,000 bbl at $27, forward now $23, 5% for 2 months → exposure $396,694, and the long may default.
Call payoff = max(S - X, 0) x qty Put payoff = max(X - S, 0) x qty Buyer profit = payoff - premium Writer profit = premium - payoff Intrinsic (call) = max(S - X, 0) Time value = premium - intrinsic Break-even: long call X + prem, long put X - prem Put-call parity: C + X/(1+r)^t = P + S
Section B only, ABC Ltd.: strike ₹30, lot 100, 50 lots = 5,000 shares, premium ₹3.05 → total premium ₹15,250, break-even ₹33.05, buyer +₹9,750 at ₹35 and +₹34,750 at ₹40. Seller is the exact opposite.
ITM/ATM/OTM: call ITM when S > X, put ITM when S < X, ATM when S = X. A call and a put at the same strike are always on opposite sides of the money.

Foreign exchange

Spread % = ((Ask - Bid) / Ask) x 100 Forward = Spot x (1 + r_quote) / (1 + r_base) Change % = (new - old) / old x 100 Law of one price: E = P_domestic / P_foreign
Worked: bid ₹83.40 / ask ₹83.50 → spread 0.12%. Spot JPY/USD 110.86, 180-day rates 0.2% Japan and 1.8% US → forward 109.98, a discount on the dollar, so the yen appreciates.
The higher-interest currency trades at a forward discount. If your answer contradicts that, the ratio is upside down.
Appreciation both ways: euro $1.18 → $1.32 is an 11% euro appreciation and an 11% dollar depreciation, using 0.76 = 1/1.32 and 0.85 = 1/1.18. Invert before computing the second figure; the two will not match exactly.
Five rows: domestic price level up → depreciate · trade barriers up → appreciate · import demand up → depreciate · export demand up → appreciate · productivity up → appreciate.
Worked Indian examples: phone ₹16,000 → ₹20,000 at ₹80/$ makes it $250 not $200. US car $10,000 = ₹8,00,000; 50% tariff → ₹12,00,000, so the rupee appreciates. 1 m barrels at $100 at ₹80 = ₹800 crore of dollar demand, so the rupee depreciates.
Six spread factors: liquidity, volatility, instrument type (majors versus exotics), market hours, dealer competition, order size. Plus central bank intervention.

The RBI and monetary policy

CRR amount = CRR% x NDTL (~4.5%) SLR amount = SLR% x NDTL (~18%) Lendable = NDTL x (1 - CRR% - SLR%) Credit multiplier = 1 / (CRR% + SLR%) = 4.44 Repo interest = principal x rate x days / 365
LAF corridor: SDF is the floor, policy repo rate in the middle, MSF the ceiling, 25 basis points either side. Bank rate now aligned with the MSF.
Tools: CRR, SLR, repo and reverse repo, MSF, base rate, bank rate. Quantitative tools change the total credit; qualitative tools (credit rationing, moral suasion, margin requirements) change its direction.
OMO purchase injects reserves, an OMO sale absorbs them. LAF plus OMOs is now the principal operating procedure; CRR is used sparingly.
RBI functions: issuing currency, banker to the banks, banker to the government, regulator and supervisor, developmental role, custodian of gold and forex reserves, controller of credit and money supply. Plus OMOs, moral suasion, credit rationing, and lender of last resort.
Structure: Central Board for four years, Governor plus up to four Deputy Governors as official directors, fifteen non-official directors, four local boards at Mumbai, Kolkata, Chennai and New Delhi. RBI Act 1934, Banking Regulation Act 1949.
MPC: six members, three RBI (Governor as chair) and three external for four years, one member one vote, Governor holds the casting vote. Target 4% CPI ± 2 points; three consecutive quarters outside triggers a failure report. Check against your class slides.

Indian banking and bank ratios

Dates: 1934 RBI Act · 1949 Banking Regulation Act · 1 July 1955 Imperial Bank becomes SBI · 1969 14 banks nationalised (deposits ≥ ₹50 crore) · 1980 6 more, over 90% in the public sector · 1975 Narasimham recommends RRBs · 1991 reforms and new private-sector banks.
RRB capital: central 50%, state 15%, sponsoring public sector bank 35%. Area limited to one region, lower lending rates, intended to eliminate money lenders, supplements cooperative banks, all states except Goa and Sikkim.
Cooperative banks: no profit no loss, Cooperative Credit Societies Act 1904, three characteristics — customer owned entity, democratic control, profit allocation.
Six functions of a bank: accepting deposits, making advances, credit creation, agency functions, general utility functions, banking services.
CASA = (current + savings) / total deposits Deposits are 75% to 85% of total liabilities Current 0% · savings 2-4% · fixed 6-8% Cost of deposits = SUM(bucket x rate) / total deposits
NII = interest earned - interest expended = 6,000 NIM = NII / earning assets = 5.88% Cost-to-income = opex / (NII + other income) = 36.14% ROA = PAT / total assets = 2.16% ROE = PAT / equity = 25.98% Loan-to-assets = gross advances / total assets = 72.84% ICR = EBIT / interest expense ROE = ROA x leverage
CD = gross advances / deposits = 92.35% LCR = HQLA / 30-day net outflows = 120.4% (min 100%) HQLA = cash with RBI + HFT + 70% of AFS Outflows = 10% of deposits + 15% of borrowings SLR = govt securities / NDTL = 19.5% CRR = cash with RBI / NDTL = 7.29% CET1 = capital + reserves - deductions = 8,530 RWA = credit + market + operational = 84,000 CET1 ratio = 10.15% (min 8%)
Gross advances = net advances + provisions, here 74,300 + 4,200 = 78,500. Earning assets = gross advances + all investments + balances with banks = 1,02,000. Risk weights: govt bonds 0%, corporates 100%, retail and SME 75%, mortgages 35-50%.
V = SUM E(CFt)/(1+k)^t TV = CF(n)(1+g)/(k - g) PV(TV) = TV/(1+k)^n
Worked valuation: ₹100, ₹120, ₹140 crore at 10% → ₹295 crore. With year 3 at ₹150 crore and g = 4%: CF4 = 156, TV = ₹2,600 crore, PV(TV) = ₹1,954 crore, V = ₹2,257 crore.

Risk, NPAs and Basel

Four risks: credit, market, operational, liquidity. Credit VaR is loss from credit events; Market VaR is loss from market price movements.
Credit risk techniques: appraisal, ratings and scoring · collateral, guarantees, credit insurance · diversification across sectors, geographies, borrower types · NPA monitoring and early warning · capital adequacy under Basel.
Market risk techniques: VaR, stress testing, sensitivity analysis · hedging with forwards, swaps and options · trading limits and stop-loss triggers · Basel III requirements.
Ladder: Standard · Sub-standard (NPA ≤ 12 months) · Doubtful (sub-standard > 12 months: DA-1 ≤ 1 yr, DA-2 1-3 yrs, DA-3 > 3 yrs) · Loss (Section A: not linked to age; Section B: over 36 months).
Sub-standard secured 15% Sub-standard unsecured 25% Doubtful 100% x (outstanding - realisable security) Loss 100%, and write off Net NPA ratio = (GNPA - Prov)/(Gross Adv - Prov) x 100 Provision coverage = Provisions / GNPA
Indian numbers: GNPA ₹10.25 lakh crore at 31 Mar 2018, 11.8% of loans. Gross and net ratios fell from 11.5% and 6.1% (Mar 2018) to 3.9% and 1.0% (Mar 2023). ₹13,22,309 crore written off over ten years; of ₹5,86,891 crore written off in three years only ₹1,09,196 crore, 18.60%, recovered.
Reasons, external: ineffective recovery tribunals, wilful defaults, natural calamities, industrial sickness, lack of demand, policy change. Internal: defective lending process, inappropriate technology, improper SWOT, poor credit appraisal, managerial deficiencies, no regular industrial visits.
CAR = (Tier I + Tier II) / RWA (min 8%)
Basel I (1988): stability plus a level playing field. Tier I core capital, Tier II supplementary (not short-term unsecured debt). Five limitations: limited credit-risk differentiation, static default risk, no term structure, simplified counterparty risk, no portfolio diversification.
Basel II: three pillars — minimum capital, supervisory review, market discipline. Adds operational risk. Approaches: standardised, foundation IRB, advanced IRB; BIA, standardised, AMA for operational risk.
Basel III: absorb shocks, better risk management and governance, stronger disclosure. Seven changes: better capital quality, capital conservation buffer, countercyclical buffer, higher common equity and Tier I, leverage ratio, liquidity ratios, SIFI treatment.

Funds, insurance and pensions

NAV = (market value of assets - liabilities) / units outstanding
Worked: ($100 m − $3 m) / 10.765 m = $9.0107 per share. (₹42,00,000 − ₹1,00,000) / 3,00,000 = ₹13.67 per unit.
Amount invested = investment x (1 - front-end load) Net return = gross - operating expense ratio Ending value = amount invested x (1 + net return)^n SIP average cost = total invested / total units
Cost chart: ₹100 at 10% for 40 years → ₹4,526 with no cost, ₹3,141 with a 1% cost, ₹1,152 with 1% cost and 30% tax. OER 0.2% to 2%; front-end, back-end and 12b-1 loads; no-load funds.
Indian structure: sponsors execute a trust deed → trust under the Indian Trusts Act 1882 → trustees → AMC (appointed by trustees with SEBI approval, seed capital 1% capped ₹50 lakh, net worth ₹50 crore, half the board independent, no other business) plus fund accountants, RTA, custodian, distributors.
Three classifications: structure (open ended, closed ended, interval) · objective (debt, equity, hybrid) · style (passive, active). SEBI categorises open-end schemes as equity, debt, hybrid, solution oriented, other. Risk-o-Meter: six levels.
Closed-end funds have a fixed share count and trade at a premium or, typically, a discount to NAV. Hedge funds against mutual funds: $1 million minimum, 1-2% plus up to 10% performance fee, leverage as a hallmark, no disclosure, no valuation rules, one-year lock-in.
Sharpe = (Rp - Rf) / sigma_p total risk Treynor = (Rp - Rf) / beta_p systematic risk Jensen = Rp - [Rf + beta_p (E(RM) - Rf)]
Sharpe for an entire portfolio, since it penalises being undiversified. Treynor and Jensen for a holding being added to an existing portfolio; Treynor standardises excess returns by beta; both need a beta estimate and betas differ by source. Rankings can differ, and that is the finding.
Insurance: pooling risk across individuals and businesses. Regulator IRDAI. Life, general, reinsurance.
NPS: voluntary, long-term, regulated by PFRDA. Tier I mandatory, restricted withdrawal, tax benefits; Tier II optional, flexible, no tax benefits. E / C / G / A, equity capped 75% in auto choice; active or auto choice by age. At 60: up to 60% tax-free lump sum, minimum 40% annuity. Returns 8-10%, market-linked.

Traps that cost marks

Name your side before any forward or option arithmetic. "You sell forward" makes you the short.
A margin call restores equity to the initial margin, not to the maintenance level. Test the call on equity, never on the price.
Option questions: read whether it asks for payoff (before premium) or profit (after). Compute the number of shares first.
Spread divides by the ask. Forward rate puts the quote currency's rate on top. Match interest rates to the tenor.
Appreciation and depreciation percentages are not mirror images. Invert both rates before computing the second one.
Gross advances, not net, in the CD ratio, the NIM denominator and credit RWA. Gross = net + provisions.
Deduct the deferred tax asset before dividing for CET1. Add all three RWA categories.
Net NPA ratio takes provisions off the numerator and the denominator. Doubtful assets are provided at 100% of the uncovered portion only.
Jensen's alpha subtracts the CAPM prediction, not the market return. NAV subtracts liabilities before dividing by units.
Show every line and give units. This is a pen-and-paper paper.

Formula cards

Contract value

Contract value = number of lots x lot size x price of the underlying

Any futures or options question. This is the exposure, not the cash required, and single units cannot be traded because the lot size is standardised.

lot size: Standardised quantity of the underlying that one contract represents
price: Price of the underlying, or the index level

Margin, leverage and the wipe-out move

Initial margin = margin % x contract value Leverage = contract value / margin = 1 / margin % Adverse move that erases the margin = margin %

To turn a contract value into the cash actually at stake, and to say how far the underlying can move before the position is in trouble.

margin %: Initial margin as a percentage of the entire contract value

Compound annual growth rate

CAGR = (Final / Initial)^(1/n) - 1

Reading the turnover and volume statistics on the India derivative-boom slides. Never divide total growth by the number of years.

n: Number of years between the two figures

Forward payoff

Long: profit per unit = S(T) - F(0,T) Short: profit per unit = F(0,T) - S(T) Total = profit per unit x quantity

Any forward or futures profit question. Decide your side first: buying forward makes you the long, selling forward the short.

S(T): Spot price of the asset at delivery
F(0,T): Forward price agreed at the start, for delivery at T

Default-risk exposure on a forward

Exposure at time t = PV{ |F(0,T) - F(t,T)| }, 0 < t < T

When a question asks who has the incentive to default and how much is at stake. The defaulting party is the one for whom the contract is a liability.

F(t,T): Today's forward price for delivery on the original delivery date T
PV: Present value, discounting from T back to t at the rate for that tenor

Margin account, one day at a time

Contract value = lot size x number of lots x price Initial margin = margin % x contract value MTM (long) = (today - yesterday) x quantity MTM (short) = (yesterday - today) x quantity Equity = previous equity + MTM + variation margin Call fires when equity < maintenance margin Variation margin = initial margin - equity

Every mark-to-market table. Work one row at a time and never skip the equity line, because the call is tested on equity, not on the price.

quantity: Units controlled: lot size times number of lots
maintenance margin: Minimum equity that must be kept in the account
variation margin: Top-up called for, sized to restore equity to the initial margin

Price move that triggers the first call

Cushion = initial margin - maintenance margin Adverse move allowed per unit = cushion / quantity

When asked how far the price can go before a margin call. Convert the equity cushion into a price move using the number of units, never the number of lots.

cushion: Equity available above the maintenance level

Option payoff and net profit

Call payoff = max(S - X, 0) x quantity Put payoff = max(X - S, 0) x quantity Buyer net profit = payoff - total premium Writer net profit = total premium - payoff quantity = number of lots x lot size

Every option numerical. Compute the number of shares first, because both the premium and the payoff are quoted per share. Read whether the question wants payoff or profit.

S: Spot price of the underlying at exercise or expiry
X: Strike or exercise price
total premium: Premium per share times the number of shares

Intrinsic value and time value

Intrinsic value (call) = max(S - X, 0) Intrinsic value (put) = max(X - S, 0) Time value = premium - intrinsic value

When a question gives a premium and asks how much of it is real value. Time value is zero at expiry, so the premium then equals the intrinsic value.

intrinsic value: Cash flow from exercising immediately, floored at zero
time value: What the market charges for the chance of a further favourable move

Break-even spot price

Long call: S = X + premium per share Long put: S = X - premium per share

Whenever the question asks where the buyer starts to profit. The lot size cancels, so work in per-share terms.

premium per share: The quoted premium, not the total paid

Put-call parity

C + X / (1 + r)^t = P + S

To price one option from the other three quantities, or to spot an arbitrage. Not derived in either section's material, so confirm it against your class slides.

C: Price of a European call, strike X, expiry t
P: Price of a European put, same strike and expiry
r: Risk-free rate for the tenor t

Reading and inverting a quote

Pair BASE/QUOTE = n means 1 unit of BASE costs n units of QUOTE Base to quote: multiply by n Quote to base: divide by n Indirect quote = 1 / direct quote

Every conversion. Name the base currency before touching the arithmetic, and sanity-check the answer's size against the weaker currency.

BASE: First currency in the pair, the single unit being priced
QUOTE: Second currency, how much of it buys one base unit

Bid-ask spread

Spread % = ((Ask - Bid) / Ask) x 100 Dealer's earnings = (Ask - Bid) x quantity

Whenever two rates are quoted. Divide by the ask. A narrow spread means high liquidity and low transaction cost; a wide one means lower liquidity or higher risk.

Bid: Rate at which the bank buys foreign exchange, the lower rate
Ask (offer): Rate at which the bank sells, the higher rate

Covered interest rate parity

Forward rate = Spot rate x (1 + r_quote) / (1 + r_base)

To find the no-arbitrage forward rate, or to test whether a quoted forward is mispriced. Convert annualised rates to the forward's tenor first: halve for 180 days, quarter for 90.

r_quote: Risk-free rate on the quote currency, for the forward's tenor
r_base: Risk-free rate on the base currency, for the same tenor

Appreciation and depreciation

Change % = (new value - old value) / old value x 100 For the other currency: invert both rates first, then apply the same formula

Any question about how much a currency has moved. The two currencies' percentages are never equal, so compute each on its own denominator.

old value: Starting rate, expressed in the units of the currency whose change you want

Law of one price

P_domestic = E x P_foreign E = P_domestic / P_foreign

When two prices for the same good are given in different currencies and you need the rate, or when a rate is given and you must test whether the law holds.

E: Exchange rate, units of one currency per unit of the other; write the units before dividing
P_domestic: Price of the identical good in the domestic currency
P_foreign: Price of the same good in the foreign currency

Purchasing power parity

Domestic price level up 10% => domestic currency down 10% Parity rate = domestic basket price / foreign basket price With inflation in both: new rate = old rate x (1 + i_domestic) / (1 + i_foreign)

Long-run exchange-rate questions. What matters is relative inflation, so never apply the domestic rate alone when both are given.

i_domestic: Domestic inflation over the period
i_foreign: Foreign inflation over the same period

Tariff pass-through

Landed price = foreign price x exchange rate Post-tariff price = landed price x (1 + tariff rate)

Trade-barrier questions. Apply the tariff to the landed rupee price, not to the foreign-currency price, and then ask what has happened to the demand for foreign currency.

tariff rate: Ad valorem duty as a fraction of the landed value

Currency demand from a trade flow

Foreign currency needed = quantity x foreign unit price Domestic currency to be exchanged = that figure x exchange rate 1 crore = 10 million

Import-demand and export-demand questions. Use the net flow when both imports and exports are given, because export receipts are sold back into the domestic currency.

net flow: Imports less exports, in foreign currency

CRR, SLR and lendable funds

CRR amount = CRR% x NDTL SLR amount = SLR% x NDTL Lendable funds = NDTL x (1 - CRR% - SLR%)

Whenever a question gives NDTL and the two ratios. CRR is cash with the RBI and earns nothing; SLR is government securities and earns a return but cannot be lent.

NDTL: Net demand and time liabilities, in practice approximated by total deposits
CRR%: Cash Reserve Ratio, about 4.5%
SLR%: Statutory Liquidity Ratio, about 18%

Credit multiplier

Credit multiplier = 1 / (CRR% + SLR%) Total credit created = fresh reserves x multiplier

When asked how much credit the banking system can create from an injection, or what a change in a ratio does to total credit. An OMO purchase injects reserves; a sale absorbs them.

fresh reserves: New cash entering the banking system, from an OMO purchase, a CRR cut or a deposit inflow

Cost of a repo or MSF borrowing

Interest = principal x rate x days / 365

Any liquidity-window question. Use the repo rate for normal borrowing and the MSF rate beyond the limit; the difference between them is the penalty for going to the ceiling.

days: Tenor of the repo, most often 1 day but auctions run to 14 days and longer

The LAF corridor

SDF (floor) = repo - spread MSF (ceiling) = repo + spread Corridor width = MSF - SDF

When asked where the overnight rate can sit. The spread has been 25 basis points on each side, so the corridor is 50 basis points wide and slides with the policy repo rate.

spread: Distance from the policy repo rate to each edge of the corridor

RRB capital split

Central government 50% · State government 15% · Sponsoring public sector bank 35%

Any question on regional rural banks. The three shares must sum to the whole capital, which is the check to run before writing the answer.

sponsoring bank: The public sector bank that sponsors the RRB and contributes 35% of its capital

Credit creation

Total deposits = fresh deposit / reserve ratio Total credit created = total deposits - fresh deposit Deposit multiplier = 1 / reserve ratio After n rounds: first loan x (1 - (1-r)^n) / r

Whenever a fresh deposit and a reserve ratio are given. Read whether the question asks for total deposits or total credit, because they differ by the original deposit.

reserve ratio: Fraction of every deposit not lent on; in India CRR plus SLR
n: Number of lending rounds, when the cascade is cut short

Lendable funds at one bank

Lendable = deposits x (1 - CRR% - SLR% - vault cash%) Maximum credit-deposit ratio = lendable / deposits

When a question asks what a single bank can lend, as opposed to what the system can create. Add every reserve percentage before multiplying once.

vault cash%: Cash held at branches for operations, over and above the CRR

CASA ratio

CASA ratio = (Current account deposits + Savings account deposits) / Total deposits

Any question on the cost or the stability of a bank's funding. Only current and savings go on top; fixed, recurring and term deposits are in the denominator only.

Current accounts: Demand deposits paying 0% interest
Savings accounts: Demand deposits paying usually 2% to 4%

Weighted average cost of deposits

Cost = (SUM of each bucket x its rate) / total deposits Saving from a mix shift = amount shifted x (old rate - new rate)

When a deposit mix and its rates are given. Divide by total deposits, not by the interest-bearing ones, or the zero-cost current accounts will vanish from the answer.

bucket: Current, savings or term deposits, each with its own rate

Net interest income from a balance sheet

Interest earned = advances x lending rate + SLR securities x their yield + 0 x CRR cash Interest paid = CASA x CASA rate + term deposits x term rate NII = interest earned - interest paid

When a question builds a bank from its deposit mix and reserve requirements. The CRR balance is non-earning, so it appears on the asset side with a yield of zero and still has to be funded.

advances: Deposits times (1 - CRR% - SLR%), when the bank lends to its limit

Bank valuation with a terminal value

V = SUM E(CFt) / (1 + k)^t CF(n+1) = CF(n) x (1 + g) TV at year n = CF(n+1) / (k - g) PV(TV) = TV / (1 + k)^n V = PV(forecast years) + PV(TV)

Any bank valuation question. Discount each year separately, grow the last forecast year once to get the terminal numerator, and discount the terminal value by (1+k)^n where n is the last forecast year.

E(CFt): Expected free cash flow to equity in period t
k: Required rate of return, that is the cost of equity
g: Stable terminal growth rate, which must be less than k

Profitability ratios

NII = interest earned - interest expended NIM = NII / earning assets Earning assets = gross advances + all investments + balances with banks Cost-to-income = operating expenses / (NII + other income) ROA = PAT / total assets ROE = PAT / (share capital + reserves) Loan-to-assets = gross advances / total assets ICR = EBIT / interest expense ROE = ROA x leverage

Reading a bank's P&L. Watch three denominators: earning assets exclude cash and fixed assets, total income is NII plus other income, and ROA uses total assets while NIM uses earning assets only.

gross advances: Net advances plus closing provisions
leverage: Total assets divided by equity

Liquidity ratios

CD ratio = gross advances / total deposits LCR = HQLA / net cash outflows over 30 days (min 100%) HQLA = cash with RBI + HFT + 70% of AFS Net outflows = 10% of deposits + 15% of borrowings SLR = government securities / NDTL (req ~18%) CRR = cash with RBI / NDTL (req ~4.5%)

Scoring a bank on liquidity. NDTL is approximated by deposits in the professor's problem. Government securities for the SLR are HTM plus 70% of AFS.

HQLA: High-quality liquid assets, convertible into cash easily and quickly
run-off rate: Fraction of a funding source assumed to leave in a 30-day stress

Capital adequacy

CET1 = share capital + reserves and surplus - deductions Total RWA = credit RWA + market RWA + operational RWA Credit RWA = SUM (exposure x risk weight) CET1 ratio = CET1 / total RWA (min 8%) CAR = (Tier I + Tier II) / RWA

Capital questions. Deduct the deferred tax asset before dividing, and add all three RWA categories. Risk weights: government bonds 0%, corporate loans 100%, retail and SME 75%, mortgages about 35% to 50%.

deductions: Items that cannot absorb loss, notably the deferred tax asset
risk weight: Regulatory multiplier reflecting the riskiness of the counterparty

Provisioning norms

Sub-standard, secured: 15% of outstanding Sub-standard, unsecured: 25% of outstanding Doubtful: 100% x (outstanding - realisable value of security) Loss: 100% of outstanding, and write off

Any provisioning question. The two traps: 25% not 15% when the exposure is unsecured, and for doubtful assets the uncovered portion only, with the security valued on a realistic basis.

realisable value: What the security would actually fetch, estimated realistically, where the bank has valid recourse

NPA ratios

Gross NPA ratio = Gross NPAs / Gross Advances x 100 Net NPAs = Gross NPAs - Provisions Net Advances = Gross Advances - Provisions Net NPA ratio = Net NPAs / Net Advances x 100 Provision coverage ratio = Provisions / Gross NPAs x 100

Any asset-quality question. Provisions come off the numerator and the denominator of the net ratio; deducting them from the top only overstates the ratio.

Provisions: Amount already set aside to cover potential loan losses
Net NPA: The actual burden on the bank after provisions and recoveries

Capital adequacy ratio

CAR = (Tier I capital + Tier II capital) / RWA Minimum under Basel I: 8% Capital needed for a target ratio = target x RWA RWA allowed at a target ratio = capital / target

Capital questions, including how much capital to raise or how much RWA to shed to reach a target. Moving exposure from a 100% weight to a 0% weight cuts RWA rupee for rupee.

Tier I: Core capital: stock issues and declared reserves
Tier II: Supplementary capital: investment gains, long-term debt over five years, hidden reserves; not short-term unsecured debt

Net asset value

NAV = (Market value of assets - Portfolio liabilities) / Units outstanding Value of a holding = units held x NAV

Every mutual fund numerical. Net the liabilities off the assets before dividing. Assets include investments, money market instruments, cash and receivables; liabilities include expenses payable, management fees and accrued liabilities.

units outstanding: Total units issued to all investors on that date

Costs, loads and compounding

Amount invested = investment x (1 - front-end load) Net return = gross return - operating expense ratio Ending value = amount invested x (1 + net return)^n After-tax net return = (gross - OER) x (1 - tax rate)

Cost questions. Deduct the load once, at the start, and the expense ratio every year. Never subtract the expense ratio from the ending value: it compounds against you.

OER: Operating expense ratio, 0.2% to 2% of average net assets
n: Number of years held

SIP average cost

Units in a month = monthly amount / NAV that month Average cost per unit = total invested / total units

Any SIP question. The average cost is always at or below the simple average of the NAVs, because a fixed rupee amount buys more units at a low NAV. Averaging the NAVs is the error to avoid.

monthly amount: The fixed rupee instalment, invested on the stated date each period

AMC requirements

Seed capital = min(1% of amount raised, Rs 50 lakh) Net worth >= Rs 50 crore at all times Independent directors >= 50% of the board

Questions on the SEBI structure. Compute the 1% first, then apply the ₹50 lakh cap, which binds for any scheme raising more than ₹50 crore.

amount raised: Money collected in all open-ended schemes of the fund

Sharpe ratio

Sharpe ratio = (Rp - Rf) / sigma_p

Evaluating an entire portfolio, because it measures total risk and therefore penalises a portfolio for being undiversified.

Rp: Portfolio return over the period
Rf: Risk-free rate
sigma_p: Standard deviation of the portfolio's return, that is total risk

Treynor ratio

Treynor ratio = (Rp - Rf) / beta_p

Evaluating a security or portfolio for possible inclusion into an existing portfolio, where specific risk will be diversified away and only systematic risk matters.

beta_p: Portfolio beta, measuring systematic risk only

Jensen's alpha

alpha_p = Rp - [ Rf + beta_p (E(RM) - Rf) ] = actual return - CAPM risk-adjusted predicted return

To say by how much a portfolio beat the market after adjusting for the risk it took. Build the CAPM prediction first; subtracting the market return instead is the standard error.

E(RM): Expected or realised market return
E(RM) - Rf: Market risk premium

NPS withdrawal at 60

Maximum tax-free lump sum = 60% of corpus Minimum annuity purchase = 40% of corpus Equity cap in auto choice = 75%

Any NPS numerical. The 60% is a maximum and the 40% a minimum, so a subscriber may annuitise more but never less.

corpus: Accumulated value of the Tier I account at retirement

Back to Money & Banking