25503 Investment Analysis Tutorial 课堂作业 代写

Finance Discipline Group

Finance Discipline Group

UTS Business School

25503 Investment Analysis

Tutorial 10

1. (a) What is meant by cash matching? Why is this not the most preferable method

for immunization?

(b) What does duration measure?

(c) What does immunization mean?

(d) What is immunization intended to accomplish? What is meant by the term

reimmunization?

(e) Consider a pure discount bond (no coupon payments) with a maturity of 4

years. The current yield-to-maturity is 9%. If the yield suddenly changes to

8.5%, how would the Macaulay duration respond to such a change?

(f) Suppose we have matched the maturity and present value of a single-payment

liability with the same characteristics of a coupon bond. When we make the

match, the yield curve is flat at 7%. Immediately after making the match, the

yield curve shifts to 8% (still flat).

i. What would be the result of such a change?

ii. Was the strategy appropriate to help you achieve an immunized position?

2. Assume you have a liability with three required payments: $3,000 due in 1 year;

$2,000 due in 2 years; and $1,000 due in 3 years.

(a) What is the Macaulay duration of this liability at a 20% (annually com-

pounded) rate of interest?

(b) What about at a 5% (annually compounded) rate of interest?

3. Assume the following characteristics for a particular bond: A face value of $1,000;

annual coupon payments of $60 (the first payment due in 1 year); an internal yield-

to-maturity of 7% (compounded annually); and a three year term.

(a) Compute the Macaulay duration of the bond.

(b) Given your answer above, compute the approximate change in the bond’s value

if the yield fell to 6.5%.

(c) Now compute the actually change in the bond’s value. Comment on the dif-

ference.

4. A 12% coupon paying bond with a face value of $100 and 2 years to maturity has a

yield of 8%. What is its duration? Assume semi-annual coupons and semi-annual

compounding.

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5. Suppose you are faced with a liability requiring the payment of $100,000 exactly two

years from now. The following two semi-annual coupon-paying bonds are available

for investment:

Bond Maturity Coupon Face Value

1 1 year 8% $100

2 3 years 10% $100

The market yield to maturity is a flat 12% per annum, with semi-annual compound-

ing.

(a) What is the duration of the liability, D L , and the duration of the two bonds,

D 1 and D 2 ?

(b) Suppose you want to invest now to meet the liability. How much money do

you need to put aside?

(c) Instead of randomly investing this amount into the two bonds, you decide

to form an immunizing portfolio that allows you to meet the liability even

if interest rates change. How many contracts of Bond 1 and Bond 2 do you

purchase for this portfolio?

(d) Assess the effectiveness of your immunizing portfolio if interest rates suddenly

decrease to 6%. Compare this to what would have happened had you only

invested in Bond 1.

6. You have an obligation to pay $1,000,000 ten years from now, and you would like to

make an investment that will enable you to meet this obligation. The investment

will be a portfolio containing the following two semi-annual coupon-paying bonds:

Bond Maturity Coupon Face Value

1 20 years 9% $100

2 30 years 6% $100

The market yield to maturity is a flat 9% per annum, with semi-annual compound-

ing.

(a) What is the duration of the liability and the two bonds: D L , D 1 , and D 2 ?

(Hint: Because the bonds in this question have very long maturities, com-

puting their durations is a lot of work if you do it by hand. So use Excel for

this.)

(b) How many contracts of Bond 1 and Bond 2 are in your immunizing portfolio?

(c) Analyze the effectiveness of your hedge if all yields change to 8% and to 10%,

respectively.

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Finance Discipline Group

UTS Business School

25503 Investment Analysis

Tutorial 11

1. In selecting a measure of performance, why do we want a measure that is insensitive

to the risk of the investment?

2. Suppose the returns and corresponding beta values for two assets (A and B) were

as indicated on the following graph:

25503 Investment Analysis Tutorial 课堂作业 代写

25503 Investment Analysis Tutorial 课堂作业 代写

(a) Compute the Treynor Index for A and B. Interpret the results.

(b) Compute the Jensen Index for A and B. Interpret the results.

(c) Suppose one manager had selected a portfolio represented by A and another

manager had selected a portfolio represented by B. Would you feel confident

in evaluating the manager’s relative performance with the Treynor or Jensen

results? Explain.

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3. Refer to the following graph:

(a) Compute the Sharpe Index for B. How would you interpret this result?

(b) Compute the Sharpe Index for A. How would you interpret this result?

(c) Suppose you decided that the “no-borrowing” version of the CAPM was the

appropriate model (see Lecture 6). How would your interpretation of A’s

performance be affected?

(d) Suppose you were presented with an asset having a beta of 0.5 and an expected

return of 7.5%. What could you conclude about the Jensen Index of this asset?

4. We are given the following information:

Observed return Beta Residual Variance

Portfolio 1 0.15 1.3 0.00

Portfolio 2 0.09 0.9 0.04

25503 Investment Analysis Tutorial 课堂作业 代写

25503 Investment Analysis Tutorial 课堂作业 代写

The standard deviation of the market is 0.3, r F = 0.05 and E[r M ] = 0.10.

(a) Compute the Jensen Index for portfolios 1 and 2. Interpret the results.

(b) Compute the Treynor Index for portfolios 1 and 2. Interpret the results.

(c) Compute the Sharpe Index for the market portfolio.

(d) Compute the Sharpe Index for portfolios 1 and 2. Interpret the results.

5. You begin a job with a medium-sized financial firm. Your firm has a number of

clients who are risk averse, but in a tremendous bull market the firm pulls in a

whopping 33% on the portfolio for the pension fund of the local tractor-drivers.

You are assigned to present the “great” news to the head of the local tractor-

drivers, but when you arrive and present the news, his face looks grim and he tells

you the return signals too much risk. What should be your plan of attack to your

clients?

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6. Two managers both are awarded a Jensen Index of 3% on their performances.

(a) Does this indicate a good performance or a poor performance?

(b) What line is used as the benchmark for this index?

(c) If you were a portfolio manager who was sure your performance was superior

to the other manager’s, what shortfalls would point out in this index?

7. Fund A has a sample mean of 0.13 and fund B has a sample mean of 0.18, with the

riskier fund B having double the beta at 2.0 as fund A. The respective standard

deviations for fund A and B are 15% and 19%. The mean return for your market

index is 0.12 with a standard deviation of 8%, while the risk-free rate on the bond

market is 8%.

(a) Compute the Jensen Index for each of the funds. What does it indicate to

you?

(b) Compute the Treynor Index for the funds and the market. Interpret the results.

(c) Compute the Sharpe Index for the funds and the market.

(d) Which fund would you deem most appropriate to invest all of a clients wealth

into?

8. With a risk-free rate of 5%, and with the market portfolio having an expected return

of 10% with a standard deviation of 5%, what is the Sharpe Index for portfolio A,

with a return of 8% and a standard deviation of 10%? For portfolio B, having a

return of 12% and a standard deviation of 8%? Would you rather be in the market

portfolio or one of the other two portfolios?

9. Suppose you are asked to analyze two portfolios having the following characteristics:

Observed return Beta Residual Variance

Portfolio 1 0.15 1.5 0.02

Portfolio 2 0.10 0.5 0.00

The risk-free rate is 0.05, the return on the market portfolio is 0.12 and the standard

deviation of the market portfolio is 0.04.

(a) Compute the Jensen Index for portfolios 1 and 2.

(b) Compute the Treynor Index for portfolios 1 and 2 and the market portfolio.

(c) Compute the Sharpe Index for portfolios 1 and 2 and the market portfolio.

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25503 Investment Analysis Tutorial 课堂作业 代写