Question

You are a fund manger in RT Asset Management Fund. You manage a portfolio consist of both stocks, bonds and currencies. The following table shows information of Treasury bond market in Hong Kong (nominated in HKD) and UK (denominated in GBP).

Year	Zero-coupon bond yield (HKD)	One-year implied forward rate (HKD)	Par coupon rate (HKD)	Zero-coupon bond yield (GBP)
1	6%			3%
2		6.5%		4%
3			7%	5%

(a)  A 3-year zero-coupon Treasury bond has a face value of $100. What is the yield-to-maturity? (in%)

(b) If the yield increases by 1 basis point, what is the change in the value of this 3-year zero-coupon bond?

(c) Your bond portfolio has a large position in a 2-year corporate bond issued by an electric car company Tesly. The bond pays coupon annually with a face value of $100 million. The current bond portfolio value is $100 million with a yield to maturity of 10%.

(i) What is the coupon rate of the bond? (in %)

(ii) Is the corporate bond yield higher than the yield of a treasury bond with the same coupon rate? Why?   

a. no, corporate bond is risk free

b. yes, corporate bond have credit risk premium

c. yes, corporate bond have liquidity premium

d. option b and c are correct

(d) You are worried about the interest rate hikes that might affect the Tesly bond. What is the Macaulay duration of the bond?

(e) If the yield of Tesly bond increases by 1 basis point, what is the change in the bond’s value?

(f) Assume that the yield of Tesly bond and the yield of the 3-year zero-coupon Treasury bond always fluctuate by the same amount. Based on the information above, how many 3-year zero-coupon bonds should you short to hedge against the interest rate risk of the Tesly bond?

(g) You have some thoughts when you develop the investment strategies.

1.        The forward contract is a biased predictor of the future stock price

2.        When you buy a stock, you expect to earn compensation for the time value of money.     

3.        When you buy a stock, you expect to earn compensation for risk.

4.        When you buy a stock index forward, you expect to earn compensation for the time value of money.     

5.        When you buy a stock index forward, you expect to earn compensation for risk.

6.        When you buy a treasury bill, you expect to earn compensation for the time value of money.     

7.        When you buy a treasury bill, you expect to earn compensation for risk.

How many of the above statements are true?

(h) You also trade on the currency market. The current spot exchange rate is 10.5 HKD/GBP. The market one-year forward rate is now 10 HKD/GBP. Use positions in HKD and GBP zero-coupon bonds to capture the arbitrage profit. What would you do to capture arbitrage profit? What is the arbitrage profit per GBP on maturity date?

Answer 1

Solution:

A. YTM of Treasury bond market in Hong Kong is 7% and YTM of Treasury bond market in UK is 5%

B. Value of Bond if Yield rate is increased by 1 Basis point (ie, 0.01% as 100 basis point is equal to 1%)

Price = Face Value / (1 + r)n

where,

r = Yield

n = number of years until maturity

Price of HK Bond at 7% yield = 100/(1+7%)^3 = 81.62

Price of HK Bond at 7.01% yield = 100/(1+7.07%)^3 = 81.46

Price decreased by 0.16 HKD

Price of UK Bond at 5% yield = 100/(1+5%)^3 = 86.38

Price of UK Bond at 7.01% yield = 100/(1+5.05%)^3 = 86.26

Price decreased by 0.12 GBP

C(i) : The coupon rate of the bond is also 10% because the price of bond and face value of bond is equal. So coupon rate will be same as yield rate. (Assumption: It is considered that portfolio has only this bond as the other data is not given)

C(ii) : The answer will be option B as the  corporate bond have credit risk premium.

D. The Macaulay Duration is calculated as = Present Value of all Cash Flows/ Face Value

It will be 1 year as both Present value and face value of bond is equal.

E. If yield of bond increased by 1 basis ie 10.1%, then the value of bond will be

Cash Flow at year 1 = 10 (100*10.%)

Cash Flow at year 2 = 100 + 10 (100*10%)

Discount Factor of 10%

Year 1 = .908

Year 2 = .824

Present Value = 10*908 + 110*.824

= 99.72 Million

F. Two times of tesly bonds are to be taken as short position in zero coupon bond to hedge the interest rate risk

G. Following statements are considered as true: Point number 3 and point number 5.

H. To earn arbitrage profit we will use carry trade arbitrage theory. Where we borrow money in low interest rate currency and invest in high interest currency.

Suppose we borrow 10 million in GBP @ 3% for one year

converion value in HKD will be 105 ( spot rate is 10.5 HKD/GBP)

Invest in HKD @ 6% for 1 year.

Future value of investment 111.3 GBP (105*(1+6%))

Convert investment value in GBP = 11.13 (111.3/10)

Forward rate HKD/GBP = 10

Loan repayable amount = 10.3 (10*(1+3%)

Arbitrage profit = Investment value in GBP - Loan Repayable In GBP

=11.13-10.3

= GBP .83 Million

Authors Bio : Financial Analyst & Portfolio Manager