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Analyzing Risk and Return on Chargers Products’ Investments

Junior Sayou, a financial analyst for Chargers Products and a manufacturer of stadium benches, must evaluate the risk and return of two assets, X and Y. The firm is considering adding these assets to its diversified asset portfolio. To assess the return and risk of each asset, Junior gathered data on the annual cash flow and beginning- and end-of-year values of each asset over the immediately preceding 10 years, 2X06–2X15. These data are summarized in the table below. Junior’s investigation suggests that both assets, on average, will tend to perform in the future just as they have during the past 10 years. He therefore believes that the expected annual return can be estimated by finding the average annual return for each asset over the past 10 years.

Junior believes that each asset’s risk can be assessed in two ways: in isolation and as part of the firm’s diversified portfolio of assets. The risk of the assets in isolation can be found by using the standard deviation and coefficient of variation of returns over the past 10 years. The capital asset pricing model (CAPM) can be used to assess the asset’s risk as part of the firm’s portfolio of assets. Applying some sophisticated quantitative techniques, Junior estimated betas for assets X and Y of 1.60 and 1.10, respectively. In addition, he found that the risk-free rate is currently 7% and that the market return is 10%.

Return Data for Assets X and Y, 2X06 to 2X15

________Asset X____________ ________Asset Y____________

$ Value $ Value

Year Cash Flow Beginning Ending %ROR Cash Flow Beginning Ending %ROR

2X06 1,000 20,000 22,000 15 1,500 20,000 20,000 7.5

2X07 1,500 22,000 21,000 2.27 1,600 20,000 20,000 8

2X08 1,400 21,000 24,000 20.95 1,700 20,000 21,000 13.5

2X09 1,700 24,000 22,000 (1.25) 1,800 21,000 21,000 8.57

2X10 1,900 22,000 23,000 13.18 1,900 21,000 22,000 13.81

2X11 1,600 23,000 26,000 20 2,000 22,000 23,000 13.64

2X12 1,700 26,000 25,000 2.69 2,100 23,000 23,000 9.13

2X13 2,000 25,000 24,000 4 2,200 23,000 24,000 13.91

2X14 2,100 24,000 27,000 21.25 2,300 24,000 25,000 13.75

2X15 2,200 27,000 30,000 19.26 2,400 25,000 25,000 9.6

Total 117.35 Total 111.41

Avg. 11.74% Avg. 11.14%

Return Data for Assets X and Y, 2X06 to 2X15

________Asset X____________ ________Asset Y____________

$ Value $ Value

Year ROR% Avg Ret Differnce Dev.^2 ROR% Avg Ret Difference Dev.^2

2X06 15 11.74 3.26 10.63 7.5 11.14 (3.64) 13.25

2X07 2.3 11.74 (9.46) 89.49 8 11.14 (3.14) 9.86

2X08 21 11.74 9.22 85.01 13.5 11.14 2.36 5.57

2X09 (1.3) 11.74 (12.99) 168.74 8.6 11.14 (2.54) 6.45

2X10 13.2 11.74 1.45 2.1 13.8 11.14 2.66 7.08

2X11 20 11.74 8.26 68.23 13.6 11.14 2.46 6.05

2X12 2.7 11.74 (9.04) 81.72 9.1 11.14 (2.04) 4.16

2X13 4 11.74 (7.74) 59.91 13.9 11.14 2.76 7.62

2X14 21.3 11.74 9.51 90.44 13.8 11.14 2.66 7.08

2X15 19.3 11.74 7.52 56.55 9.6 11.14 (1.54) 2.37

Total 712.82 Total 69.49

Avg. (9) 79.20 Avg. (9) 7.72

Standard Dev. 8.9 Standard Dev. 2.8

C. Asset X Asset Y

Expected Annual Return: 11.74 11.14

Standard Deviation: 8.9 2.8

Coefficient of Variation: 0.8 0.3

d. Use the CAPM to find the required return for each asset. Compare this value with the average annual returns calculated in part a.

e. Compare and contrast your findings in parts c and d. What recommendations would you give Junior with regard to investing in either of the two assets? Explain to Junior why he is better off using beta rather than the standard deviation and coefficient of variation to assess the risk of each asset.

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Tod Thiel
Tod ThielLv2
28 Sep 2019

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Related questions

Question 1.

Consider a portfolio that has equal amounts of $10 invested in two assets. Suppose returns on the two assets are jointly normally distributed. The annual expected returns and variance or return on the first asset are given by

m1 = 0.10 s1^2 = 0.04

And those on the second asset are given by

m2 = 0.05 s2^2 = 0.03

Consider three cases:

The correlation between the return is r = 0

The correlation between the return is r = +0.50

The correlation between the return is r = -0.50

For each case, identify the 99% Value-at-Risk of the portfolio. Explain the pattern of dependence of VaR on the correlation.

Question 2.

You are given a portfolio of three assets whose returns are jointly normally distributed with the following mean vector and covariance matrix:

0.20 0.08 0.02 0.02

0.10 0.02 0.06 0.03

0.15 0.02 0.03 0.07

a. Compute the 95% VaR for the portfolio if we invest $1 in the first asset. $2 in the second asset, and $3 in the third asset.

b. How much does each asset’s holding contribute to the overall VaR risk?

Question 3.

You are given a portfolio of two assets whose returns are jointly distributed with the following vector and covariance matrix.

0.20 0.08 0.04

0.10 0.04 0.06

a. Compute the 95% VaR of the portfolio if $1 is invested in the first asset and $1 is invested in the second.

b. Compute the risk-contribution of each asset to the VaR.

c. Is the current portfolio weighting optimal? If not, suggest a better one.

a. You own a two-bond portfolio. Each has a par value of $1,000. Bond A matures in five years, has a coupon rate of 8 percent, and has an annual yield to maturity of 9.20 percent. Bond B matures in fifteen years, has a coupon rate of 8 percent and has an annual yield to maturity of 9.20 percent. Both bonds pay interest semi-annually. What is the value of your portfolio? What happens to the

value of your portfolio if each yield to maturity rises by one percentage point?

b. Rather than own a five-year bond and a fifteen-year bond, suppose you sell both of them and invest in two ten-year bonds. Each has a coupon rate of 8 percent (semi-annual coupons) and has a yield to maturity of 9.20 percent. What is the value of your portfolio? What happens to the value of your portfolio if the yield to maturity on the bonds rises by one percentage point?

c. Based upon your answers to (a) and (b), evaluate the price changes between the two portfolios. Were the price changes the same? Why or why not?

Task 2:

Construct a spreadsheet to replicate the analysis of the table. Click here to view the table. That is, assume that $10,000 is invested in a single asset that returns 7 percent annually for twenty-five years and $2,000 is placed in five different investments, earning returns of 100 percent, 0 percent, 5 percent, 10 percent, and 12 percent, respectively, over the twenty-year time frame. For each of the questions below, begin with the original scenario presented in the table:

a. Experiment with the return on the fifth asset. How low can the return go and still have the diversified portfolio earn a higher return than the single-asset portfolio?

b. What happens to the value of the diversified portfolio if the first two investments are both a total loss?

c. Suppose the single-asset portfolio earns a return of 8 percent annually. How does the return of the single-asset portfolio compare to that of the five-asset portfolio? How does it compare if the single-asset portfolio earns a 6 percent annual return?

d. Assume that Asset 1 of the diversified portfolio remains a total loss (�100% return) and asset two earns no return. Make a table showing how sensitive the portfolio returns are to a 1-percentage-point change in the return of each of the other three assets. That is, how is the diversified portfolio�s value affected if the return on asset three is 4 percent or 6 percent? If the return on asset four is 9 percent or 11 percent? If the return on asset five is 11 percent? 13 percent? How does the total portfolio value change if each of the three asset�s returns are one percentage point lower than in the table? If they are one percentage point higher?

e. Using the sensitivity analysis of (c) and (d), explain how the two portfolios differ in their sensitivity to different returns on their assets. What are the implications of this for choosing between a single asset portfolio and a diversified portfolio?

Task 3:

Annual savings from Project X include a reduction of ten clerical employees with annual salaries of $15,000 each, $8,000 from reduced production delays, $12,000 from lost sales due to inventory stock-outs, and $3,000 in reduced utility costs. Project X costs $250,000 and will be depreciated over a five-year period using straight-line depreciation. Incremental expenses of the system include two new operators with annual salaries of $40,000 each and operating expenses of $12,000 per year. The firms� tax rate is 34 percent.

a. Find Project X�s initial cash outlay.

b. Find the project�s operating cash flows over the five-year period.

Cash Flow:

Benefits:
Sale Increase: Reduced lost sales from stockouts
Cost reduction: Salary reduction delay
Reduced production delay
Reduction in utility cost

Change in eranings before depreciation:
 change in sales + cost reductions
Depreciation expense

benefits from the project:
change in sales + cost reductions
-depreciation

Cost increases:
Annual salary
operating expense
Increase in costs

Earnings before taxes:(benefits less cost increases)
Less: taxes
Earnings after taxes

Annual cash flows=net+depreciation=

C.If the project's required return is 12%, should it be implemented?

Year Cash flow PV at 12%
0
1
2
3
4
5

Please help me with this

Greta, an elderly investor, has a degree of risk aversion of A = 4 when applied to return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 8% per year, with a SD of 18%. The hedge fund risk premium is estimated at 10% with a SD of 36%. The return on each of these portfolios in any year is uncorrelated with its return or the return of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far from certain.


a-1.

Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)


S&P
Hedge


a-2.

What is the expected return on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)


Expected return


a-3.

What should be Greta’s capital allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)


S&P
Hedge
Risk-free asset

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