Financial Risk Management

Transcription

1 Review of asset liability management University of Oulu - Department of Finance Spring 2016

2 Balance sheet of a bank ASSETS e Risk factor Unfavorable scenario Cash and Receivables Cash 60 No risk USD receivables ($550) 440 Exchange rate risk Decrease in euro-price of dollar Loans Fixed rate 3660 Interest rate risk Increase in interest rates Floating rate 340 Interest rate risk Increase in interest rates Other Assets Equity investments 500 Equity price risk Decrease in equity prices Total 5000 LIABILITIES AND EQUITY Payables USD payables ($1200) 960 Exchange rate risk Increase in euro-price of dollar Deposits and Borrowings Fixed rate 1000 Interest rate risk Decrease in interest rates Floating rate 2000 Interest rate risk Decrease in interest rates Other Liabilities Written options 140 Equity price risk Change in equity prices Equity Owners Equity 900 Residual of other items Decrease in net assets Total /5000 = 18%

3 Exchange rate risk Review of asset liability management Exchange rate risk in Receivables and Payables Market risk factor: US-dollar exchange rate Risk: Increase in the euro-price of dollar Sensitivity: One-to-one Exchange rate risk Scenarios Change in exchange rate S Exchange rate S USD Receivables in EUR $550 S USD Payables in EUR $1200 S Net position in EUR $650 S

4 Managing exchange rate risk Exchange rate risk Risky position: Negative net of USD-driven assets and liabilities Risk: Increase in euro-price of dollar Insurance tools Long forward contract Call option Long forward contract Payoff at the maturity: S K Delivery price K is given by the market in terms of the forward exchange rate Initial price of the contract is zero Call option Payoff at the maturity: max(0, S X ) Strike price (insurance level) X is chosen by the buyer Initial price of the contract depends on the chosen strike price

5 Managing exchange rate risk with a forward contract Hedge with a long forward contract Current forward exchange rate is F 0 = 0.82 Delivery price is set at K = F 0 = 0.82, and remains fixed until the maturity Long forward contract offsets the change in the value of the negative net position Total position is fixed, no matter of the direction of the exchange rate change Exchange rate risk Scenarios Change in exchange rate S Exchange rate S USD Receivables in EUR $550 S USD Payables in EUR $1200 S Net position in EUR $650 S Long forward contract $650 ( S 0.82) Total position in EUR $

6 Managing exchange rate risk with a call option Hedge with a call option Strike price is chosen to be X = 0.80, and remains fixed until the maturity Call option offsets the value change above the chosen insurance level X Above insurance level the unfavorable value chance is offset by the option payoff Below insurance level the favorable effect of a decreasing rate is still maintained Exchange rate risk Scenarios Change in exchange rate S Exchange rate S USD Receivables in EUR $550 S USD Payables in EUR $1200 S Net position in EUR $650 S Long call option $650 max(0, S 0.80) Total position in EUR $650 min( S, 0.80)

7 Interest rate risk Review of asset liability management Interest rate risk in Loans, Deposits and Borrowings Market risk factor: Market interest rates Risk: Increase in interest rates Sensitivity: Duration (D) Interest rate risk Scenarios Change in interest rate r 1.0% 0.0% +1.0% Type D Fixed rate loans r Floating rate loans r Fixed rate deposits and borrowings r Floating rate deposits and borrowings r Net position r

8 Managing interest rate risk Interest rate risk Risky position: Positive net duration of interest-rate-driven assets and liabilities Risk: Increase in interest rates Insurance tools Interest rate swap Interest rate swap Buyer pays a fixed swap rate for receiving a floating rate over multiple periods Swap rate is quoted in the market Initial price of the contract is zero Duration of a swap is negative and depends on the current swap rate

9 Managing interest rate risk with a swap Fixed leg Current swap rate is 2.000% Fixed leg can be considered as a sold e1000 fixed coupon bonds with e20 annual coupons Bond initially sells at e1000 Yield-to-maturity of the bond is 1.980% in terms of continuous compounding Duration of the bond is 16.7 Value of the fixed leg is V fix = r 1000 Floating leg Floating leg can be considered as a bought e1000 floating rate bond Bond initially sells at e1000 Next coupon payment is to take place six months from now Duration of the bond is 0.5 Value of the floating leg is V flo = r 1000 Swap Buyer of the swap pays the fixed leg and receives the floating leg Value of the swap is V = V flo V fix = 16.2 r 1000 With the nominal principal of 2655 instead of 1000 it is V = V flo V fix = 16.2 r 2655

10 Managing interest rate risk with a swap Hedge with an interest rate swap Net duration of interest-rate-driven assets and liabilities is Duration of a 20-year swap is 16.2 with the current swap rate quotation of 2.000% Swap with a nominal principal of e2655 offsets the duration of the position Total position is fixed, no matter of the direction of the interest rate change Interest rate risk Scenarios Change in interest rate r 1.0% 0.0% +1.0% Type D Fixed rate loans r Floating rate loans r Fixed rate deposits and borrowings r Floating rate deposits and borrowings r Net position r year swap r Total position

11 Equity price risk Review of asset liability management Equity price risk in Other Assets Market risk factor: Equity market prices Risk: Decrease in equity prices Sensitivity: Beta (β) Equity price risk Scenarios Change in stock market R m 10% 0% +10% Type β Equity investments R m

12 Managing equity price risk Equity price risk Risky position: Equity investments in assets Risk: Decrease in equity prices Insurance tools Short index futures contract Index put option Short index futures contract Payoff at the maturity: K S Delivery price K is given by the market in terms of the futures price Initial price of the contract is zero Put option Payoff at the maturity: max(0, X S) Strike price (insurance level) X is chosen by the buyer Initial price of the contract depends on the chosen strike price

13 Managing equity price risk with an index futures contract Hedge with a short index futures contract Contract trades index points Euro-value of an index point is P = e2 Current value of the index is S 0 = 100 Delivery price is set at K = F 0 = 102, and remains fixed until the maturity Number of contracts n is determined on the basis of the target beta β Equity price risk Scenarios Change in stock market R m 10% 0% +10% Stock market index S Type β Equity investments R m Short futures contract 3 e2 (102 S) Total position K = F 0 n = (β β )V 0 ( ) 500 = = 3 PS 0 e2 100

14 Managing equity price risk with an index put option Hedge with an index put option Contract trades index points Euro-value of an index point is P = e2 Maximum allowed percentage decrease z in portfolio value is chosen Strike price X is determined on the basis of z and portfolio beta β Number of contracts n is determined on the basis of the portfolio beta β Equity price risk Scenarios Change in stock market R m 10% 0% +10% Stock market index S Type β Equity investments R m Long put option 3 e2 max(0, 100 S) Total position X = S 0 (1 + z 0% ) = 100(1 + β 1.20 ) = 100 n = βv = PS 0 e2 100 = 3

15 Market risk in written options Price risk of the sold derivative securities on the liability side Market risk factor: Equity market prices (as an example) Risk: Increase/decrease in equity prices Sensitivity: Delta Market risk in written options Scenarios Change in stock market 10% 0% +10% Stock market index S Type n Price Value Call options max(0, S 100) Put options max(0, 100 S) Total Black-Scholes prices of hypothetical index options. X = 100, σ = 0.20, r q = 0.00, T t = 0.25

16 Managing market risk in written options Derivatives price risk Risky position: Sold derivative securities Risk: Change in the underlying asset s price Insurance tools Neutralizing position in the underlying asset Delta hedging Underlying asset position is created on the basis of derivatives deltas Neutralizing asset position is rebalanced on a frequent basis Not considered here and remains to be learned

17 Forward contract risk - where it goes? 0 Buyer S T +( S T K) = K Dealer +0 ( S T K) (K S T ) = 0 0 Seller + S T +(K S T ) = K When it comes to the buyer, the seller, and the dealer both the buyer and the seller pay a fixed fee to the dealer, the buyer pays a fixed price of K, the seller receives a fixed price of K, the dealer s risky positions offset each other.

18 Option contract risk - where it goes? c Buyer S T +max(0, S T X ) = c min( S, X ) Dealer + c + p max(0, S T X ) max(0, X S T ) = +c +p S T X p Seller + S T +max(0, X S T ) = p+max( S, X ) When it comes to the buyer, the seller, and the dealer both the buyer and the seller pay the option price to the dealer, the buyer pays either a fixed price of X or a lower market price, the seller receives either a fixed price of X or a higher market price, the dealer stays with a risky position of S T X, which can be considered as a liability in the balance sheet!

19 Balance sheet effects of a scenario Changes in the market variables Exchange rate is increased from 0.80 to 0.90 Interest rate is increased by 1% Stock market is decreased by 10% Assets Value of cash remains unchanged Value of UDS-receivables increases from 440 to 495 Value of fixed rate loans decreases from 3660 to 3155 Value of floating rate loans decreases from 340 to 339 Value of equity investments decreases from 500 to 440 Value of total assets decreases from 5000 to 4489 Liabilities Value of USD-payables increases from 960 to 1080 Value of fixed rate deposits and borrowings decreases from 1000 to 928 Value of floating rate deposits and borrowings decreases from 2000 to 1996 Value of written options increases from 140 to 300 Owners equity Value of owners equity decreases from 900 to 185 Solvency decreases from 18% to 4% (185/4489)

20 Balance sheet effects of a scenario Managing the exchange rate risk Exchange rate is increased from 0.80 to 0.90 Net change in the USD-position is 65 Payoff of the forward contract is 52 Managing the interest rate risk Interest rate is increased by 1% Net change in the interest rate position is 430 Payoff of the swap is 430 Managing the equity price risk Stock market is decreased by 10% Net change in the interest rate position is 60 Payoff of the futures contract is 72 Total compensation Total payoff of the derivatives is = 554 Value of assets increases from 4489 to 5043 Owners equity increases from 185 to 739 Solvency increases from 4% to 15% (739/5043)

21 Balance sheet carrying market risks ASSETS Intial situation Without a hedge With a hedge Cash and Receivables Cash USD receivables ($550) Loans Fixed rate Floating rate Other Assets Equity investments Derivatives 554 Total LIABILITIES AND EQUITY Payables USD payables ($1200) Deposits and Borrowings Fixed rate Floating rate Other Liabilities Written options Equity Owners Equity Total