Formula Sheet

Bond Valuation

Share Valuation

Maturity Model with a portfolio of assets and liabilities

Duration

Measuring price sensitivity with duration :

If the level of interest and expected shock to interest rates are the same for both assets and

liabilities, then:

Duration and Convexity

Repricing Model on interest rate risk :

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Simple promised return on loan :

Loan rate = Base Rate + Credit risk premium or margin

Contractually Promised return on loan :

1+k = 1 + [f + (BR+m)] / [1- b(1-R)]

Expected return on loan : E(r) = p(1+k).

Term Structure Derivation of Credit Risk:

p (1+ k) = 1+ i or

[(1 - p) γ(1 + k)] + [p(1 + k)] = 1 + i

K – I = Φ = (1 + i) / (γ + p – pγ) – (1 + i)

RAROC = one year income on a loan / loan (asset) at risk or capital at risk

Loan (asset) at risk or capital at risk = DLN = -DLN x LN x (DR/(1+R))

Credit Metrics : VARone day = P × 1.65 × std dev

CreditRisk+ Model :

Concentration Limits for a Loan Portfolio:

KMV Portfolio Manager Model :

Expected return on a loan to borrower i

Risk of a loan to borrower i (σi):

Net FX exposure of an FI:= (FX assetsi – FX liabilitiesi) + (FX boughti – FX soldi)

= Net foreign assetsi + Net FX boughti

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Promised return on a loan commitment :

(f1+ f2(1-dd)+ (BR+m) dd) )/ (dd- [b(dd)(1-RR)] )

Daily earnings at risk (DEAR) = Dollar market value of the position × Price sensitivity x

Potential adverse move in yield , or

Daily earnings at risk (DEAR) = Dollar market value of the position × Price volatility

Market value at risk (VAR) = DEAR × N

DEAR for Foreign Exchange :

DEAR = dollar value of position × FX volatility

Dollar equivalent value of position = FX position × spot exchange rate

DEAR for Equities

DEAR = dollar value of position × stock market return volatility

market return volatility = 1.65 std devM.

DEAR portfolio =[DEARa2 + DEARb

2 + DEARc

2 + 2rab × DEARa *× DEARb + 2rac × DEARa

× DEARc + 2rbc × DEARb × DEARc]1/2

Liquidity Index :

Hedging Interest Rate Risk with Futures Contracts :

∆F = dollar gain or loss on a futures position for changing interest rates

Number of sold or bought contracts (NF) :

No basis risk

Adjusting for basis risk:

Where:

b = [∆RF/(1+RF)] / [∆R/(1+R)

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Hedging Foreign Exchange Risk with Futures Contracts :

• h = ΔSt /Δft

• Nf = (Long FX asset position × β)/(size of one FX contract).

• β = estimated value of h using past data.