Question

7.120 marks] Consider a five-year investment with the following annual returns and predicted variations. Year eturnT Variation (v) TTA% 0.10% 2 2.39 0.25% -0.5% 0.55% 4 +4.3% 1.25% +25%- 3.45% a5 marks] Compute the total and average annual rate of return. b13 marks] Given an initial investment of $1,000, compute the value of this investment at the end of year 5 and its total increase or decrease both in $ and %. Compare to your results in (a) (they should match). c[6 marks] Of course, any prediction on future returns is uncertain and subject to variation. Specifically, suppose thattheactualreturnineachyearisuniformlydistributed with a variation varoundthepredicted return r as its mean: r± v. Use the random numberfunctions in Exceltorandomly generate 20dfferent scenarios (e.g., in 20 different rows whose formulas you may simply copy), and compute the average total and average annual rate of returns as well as the average or expected value of this investmentat the end of year 5. Print and insert a single-page worksheet that shows all random data and calculated formulas as page 14, and another worksheet that shows all formulas as page 15. (Note: To switch between values and formulas in Excel, go to the "Formulas"tab and select the "Show Formulas"menu option.) Compare to your findings in (a)and (b), and comment (they may possibly be quite different). d[6 marks]Repeat(d)underthenewassumption thatthe actual returnin eachyearis normallydistributed with the predicted return r as its mean and the variation v as its standard deviation. Print and insert the corresponding two worksheets on pages 16 and 17. Comment or compare to your previous findings.

Answer 1

1. Total return = (1+1.4%)*(1+2.3%)*(1-0.5%)*(1+4.3%)*(1+2.6%)-1 = 10.45%

Average annual rate of return = (1.4%+2.3%-0.5%+4.3%+2.6%)/5 = 2.02%

2. At the end of 5 years, $1000 becomes = 1000*(1+1.4%)*(1+2.3%)*(1-0.5%)*(1+4.3%)*(1+2.6%) = $1104.50

Total increase = $1104.50 - $1000 = $104.50

% Increase = (104.50 / 1000)*100 = 10.45%