金融市场上期题 金融考试题 西南财经大学天府学院

Problems

1. The following table lists foreign exchange rates between US dollars and British pounds

during April.

Date 4/1 4/4 4/5 4/6 4/7 4/8 4/11 4/12 4/13 4/14 4/15

US Dollars per

GBP

1.9564 1.9293 1.914 1.9374 1.961 1.8925 1.8822 1.8558 1.796 1.7902 1.7785

Date 4/18 4/19 4/20 4/21 4/22 4/25 4/26 4/27 4/28 4/29

US Dollars per

GBP

1.7504 1.7255 1.6914 1.672 1.6684 1.6674 1.6857 1.6925 1.7201 1.7512

Which day would have been the best day to convert $200 into British pounds? Which day would have been the worst day? What would be the difference in pounds?

2. Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the

following table:

Years to Maturity 3 3 6 9 9

Discount Rate

5 7 7 7 9

Current Price

What relationship do you observe between yield to maturity and the current market value?

3. You are willing to pay $15,625 now to purchase a perpetuity which will pay you and your

heirs $1,250 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, ordinary annuity instead of a perpetuity? 4.

A bank has two, 3-year commercial loans with a present value of $70 million. The first is a $30 million loan that requires a single payment of $37.8 million in 3 years, with no other payments until then. The second is for $40 million. It requires an annual interest payment of $3.6 million. The principal of $40 million is due in 3 years.

a. What is the duration of the bank’s commercial loan portfolio?

b. What will happen to the value of its portfolio if the general level of interest rates

increased from 8% to 8.5%?

5. Consider a bond that promises the following cash flows. The required discount rate is 12%.

Year

Promised Payments

0

1 160

2 170

3 180

4 230

You plan to buy this bond, hold it for 2? years, and then sell the bond.

a. What total cash will you receive from the bond after the 2? years? Assume that periodic

cash flows are reinvested at 12%.

b. If immediately after buying this bond, all market interest rates drop to 11% (including

your reinvestment rate), what will be the impact on your total cash flow after 2? years? How does

this compare to part (a)?

c. Assuming all market interest rates are 12%, what is the duration of this bond?

Solution:

a. You will receive 160, reinvested that for 1.5 years, and 170 reinvested for 0.5 years.

Then you will sell the remaining cash flows, discounted at 12%. This gives you:

160?(1.12)1.5?170?(1.12)0.5?180230??$733.69. 1.120.51.121.5180230??$733.74. 0.51.51.111.11b. This is the same as part (a), but the rate is now 11%.

160?(1.11)1.5?170?(1.11)0.5?

Notice that this is only $0.05 different from part (a).

6. You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan on

selling the bond in one year, and believe that the required yield next year will have the

following probability distribution: Probability 0.1 0.2 0.4 0.2 0.1

Required Yield

6.60% 6.75% 7.00% 7.20% 7.45%

a. What is your expected price when you sell the bond? b. What is the standard deviation?

Multiple Choice

1.When the inflation rate is expected to increase, the real cost of borrowing declines at any given interest rate; as a result, the _________ bonds increases and the _________ curve shifts to the right.

A) demand for; demand B) demand for; supply C) supply of; demand D) supply of; supply

In Figure 4.1, the most likely cause of the increase in the equilibrium interest rate from i1 to i2 is A)an increase in the price of bonds. B) a business cycle boom.

C) an increase in the expected inflation rate. D) a decrease in the expected inflation rate.

In Figure 4.2, one possible explanation for the increase in the interest rate from i1 to i2 is a(n) _________ in _________.

A) increase; the expected inflation rate B) decrease; the expected inflation rate C) increase; economic growth D) decrease; economic growth

Solution:

Years to Maturity Yield to Maturity Current Price 3 5 $1,054.46 3 7 $1,000.00 6 7 $1,000.00 9 5 $1,142.16 9 9 $ 880.10

When yield to maturity is above the coupon rate, the band’s current price is below its face

value. The opposite holds true when yield to maturity is below the coupon rate. For a given maturity, the bond’s current price falls as yield to maturity rises. For a given yield to maturity, a bond’s value rises as its maturity increases. When yield to maturity equals the coupon rate, a bond’s current price equals its face value regardless of years to maturity.

Solution: To find your yield to maturity, Perpetuity value ??PMT/I. So, 15625 ??1250/I. I ??0.08

The answer to the final part, using a financial calculator: N ??20; I ??8; PMT ??1250; FV ??0 Compute PV : PV ??12,272.69

Solution:

a. You will receive 160, reinvested that for 1.5 years, and 170 reinvested for 0.5 years.

Then you will sell the remaining cash flows, discounted at 12%. This gives you:

160?(1.12)1.5?170?(1.12)0.5?180230??$733.69. 1.120.51.121.5180230??$733.74. 0.51.51.111.11b. This is the same as part (a), but the rate is now 11%.

160?(1.11)1.5?170?(1.11)0.5? Notice that this is only $0.05 different from part (a).

c. The duration is calculated as follows:

Year

Payments

PV of Payments

Time Weighted PV of Payments

Time Weighted PV of Payments

Divided by Price

1 160.00 142.86 142.86 0.26

2 170.00 135.52 271.05 0.49

3 180.00 128.12 384.36 0.70

4 230.00 146.17 584.68 1.06

Sum 552.67

2.50

Since the duration and the holding period are the same, you are insulated from immediate changes in interest rates! It doesn’t always work out this perfectly, but the idea is important.

Solution: The duration of the first loan is 3 years since it is a zero-coupon loan. The duration

of the second loan is as follows:

Year

Payment

PV of Payments

Time Weighted PV of Payments Time Weighted PV of Payments Divided by Price

1 3.60 3.33 3.33 0.08

2 3.60 3.09 6.18 0.15

3 43.60 34.61 103.83 2.53

41.03

2.76 Sum

The duration of a portfolio is the weighted average duration of its individual securities.

So, the portfolio’s duration ? 3/7 ? (3) ? 4/7 ? (2.76) ? 2.86 If rates increased, ?P??DUR??i0.005?P??2.86??70,000,000??926,852. 1?i1.08

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