Question

Question 1

a. Over the past twelve months, Lululemon had monthly returns of -5%, 0%, 0%, -5%, 0%, 0%,

10%, 15%, 10%, 0%, 0%, and 5%. What was the total return over this period?

b. Suppose Shake Shack returns 10% this year and -10% next year. What is the total return over this

2-year period? Explain why this is not equal to 0%. What would the return for next year have to

equal (assuming this year’s return is still 10%) for the total return over two years to be 0%?

c. Suppose a stock has returns of -2% every month. What is the total return over the course of 1

year? What is the total return over a decade?

d. Suppose a stock has a total return of 5% over the course of 5 trading days (Mon-Fri). The stock

had the same return (r) for each of these days. Solve for r. Explain why r is not equal to 1%.

Answer 1

Part - A

Total monthly return = (-5%+0%+0%-5%+0%+0%+10%+15%+10%+0%+5%) = 30%

Part - B

Here we have to know one concept i.e. Present value factor.

Return of the current year different from return of the next year. We cant add it directly, here we have to apply the concept of present value in this problem. One dollor on hand today has different value having the same in the next year.

In the given question the return of the current year return was 10% and second year return was -10%. We cant add these two returns. Suppose we have invested 100 today at the end year second year our investment will be 99. So total return is.

Investment value in Year - 1 = 100+10% = 110

Investment value in Year - 2 = 110-10% = 99

Difference in investment value = 1

Return = -1/100*1/1.10² = 0.00826% (If discounted at 10% - assumed)

If we want the total equal to Zero then second year return will be =(100/110*100) = -9.09%

PART - C

If investment value assumed 100$, montly return is negitive in this case so we will get the negitive return at the end year.

Monthly return = -2%

Yearly return = (100*98%¹² - 100) = -21.52833%

Return for the decade = (100*98%¹²⁰ - 100) = -91.49682%

PART - 4

Return for 5 working days = 5%

Return for each day is same so we can't divide the total return by 5. Every day return was increased by using compunding interest method. So it will not be 1%

r*(1+r)*(1+r)²*(1+r)³*(1+r)⁴ = 5%