Essay on Investment: Interest and Portfolio

PRACTICE EXAMS

All multiple choice questions are worth 2 points. The points for other questions are given above the corresponding question.

EVERY QUESTION CAN BE TRACED TO THE SLIDES, THE ASSIGNMENTS, AND/OR THE QUIZZES. THE IMPORTANT TAKE-AWAY IS THAT IF YOU FOLLOW WHAT WE DO IN THE SLIDES, DO YOUR ASSIGNMENTS, AND QUIZZES, THE EXAM SHOULD BE A CAKE-WALK.

Chapter 5

Answer questions 1 – 5 using the following historic data on realized returns.

You invested $1000 in Amazon.com 3 years ago. Assume that Amazon has not paid dividends during the last 3 years and it was worth $1100 two years back, $1199 one year back, and is currently worth $1438.8.

(3 points)
1. What is the 3-year holding period return?

HPR= 1438.8/1000 – 1 = 43.88%

(3 points)
2. What is the effective annual return?

EAR = (1438.8/1000)1/3 – 1 = 12.9%

(5 points)
3. What is the average annual return? r1 = 1100/1000 – 1 = 10% r2 = 1199/1100 – 1 = 9% (3) r3 = 1438.8/1199 – 1 = 20%

E(r) = (10 + 9 + 20)/3 = 13% (2)

(4 points)
4. What is the standard deviation of annual return? σ2 = 1/(3-1) * [(10 – 13)2 + (9 – 13)2 +(20 – 13)2] =37 (3) σ = 6.1% (1)

5. Which gives an accurate measure of the return you have actually earned on your investment? A) Simple average return B) Geometric average return C) Annual Percentage Return (APR) D) None of the above

(2 points)
6. You invested $1000 in APPLE 5 years ago. It is now worth $5000. What is the 5-year holding period return?

HPR= 5000/1000 – 1 = 400%

(2 points)
7. You invested $1000 in APPLE 5 years ago. It is now worth $5000. What is the effective annual return?

EAR = (5000/1000)1/5 – 1 = 37.97%

(2 points)
8. If the effective annual return is 37.97%, what is the continuously compounded effective annual return?

Continuously compounded EAR = ln(1+0.3797) = 32.19%

(2 points)
9. If the monthly return is 1% (that is, return = 1% per month), what is the APR?

APR = 12*1 = 12%

(2 points)
10. If the monthly return is 1% (that is, return = 1% per month), what is the Effective Annual Return?

EAR = (1+0.01)12 – 1 = 12.68%

(10 points)
11. If annual returns are 10%, 9%, and 20%, what is the Sharpe Ratio. Assume risk-free rate = 4%.

E(r) = (10 + 9 + 20)/3 = 13% (2) Average Excess Return = 13 – 4 = 9% (2) σ2 = 1/(3-1) * [(10 – 13)2 + (9 – 13)2 +(20 – 13)2] =37 (3) σ = 6.1% (1) S.R. = 9/6.1 = 1.48

(2 points)
12. If the annual nominal rate of interest is 5% and the expected inflation rate is 4%, what is the real rate of interest?

Real Rate = 5 – 4 = 1% (OR) 1.05/1.04 – 1 = 0.96%

13. If the annual real rate of interest is 5% and the expected inflation rate is 4%, the nominal rate of interest would be approximately A) 1%. B) 20%. C) 9%. D) 15%.

Chapter 6

(6 points)
14. You invest 125% of your wealth in a risky portfolio (by borrowing at the risk-free rate of 3%) with an expected return of 12% and a standard deviation of 15%. Compute expected return, standard deviation, and Sharpe Ratio of the complete portfolio.

E(rP) = 1.25(12%) + -0.25(3%) = 14.25% (2) σP = 1.25(15) = 18.75% (2) S.R. = (12 – 3) / 15 = 0.6 (2) OR S.R. = (14.25 – 3) / 18.75 = 0.6

(5 points)
15. Given the numbers above, draw the capital allocation line. Clearly mark the X-axis, Y-axis, appropriate portfolios and securities, and the slope of the CAL.

Slope of CAL = Sharpe Ratio of risky portfolio = 0.6

If you want to know how I created it, click the attachment.

Use the following to answer the next two questions.

Investment
Expected Return
Standard Deviation
1
0.12
0.30
2
0.15
0.50
3
0.21
0.16
4

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