Question

Investment A is an equity (stock) investment in an American company. Returns on this Investment for the past 6 years are detailed in the table below, and Carlo expects the returns of the next 6 years to be the same as the last 6 years.

Year	Return
1	+80%
2	-50%
3	+70%
4	-50%
5	+40%
6	-5%

1. With respect to Investment A, if the annual returns are each considered to be equally likely to occur, calculate the standard deviation of the returns. ____________

2. What is the expected average annual rate of return on Investment A? __________

3. An investor who invested $10,000 in Investment A at the beginning of year 1 would have how much in the investment at the end of year 6? _____________

4. Taking only the beginning and ending balances of the investment into account in order to smooth the returns and to avoid the problem of multiple rates of return that can occur when returns are both positive and negative, what is the compound annual growth rate of Investment A over the 6-year period? ____________

5. What is the relevant annual rate of return per unit of risk (expressed as one number) for Investment A over the 6-year period? _____________

Answer 1

A) Taking the returns data in excel or python

Standard deviation=Stdeva(80%,-50%,70%, -50%,40%,-5%)

That is 0.52

So the standard deviation of returns is 52%

B) Taking the initial amount as 100 RS

we have amounts in the end of the year as

year 1= 180 year 2=90 year 3 =153 year 4=76.5 year 5= 107.1

Final year 6=101.74

Average annual rate of return is (101.74/100)= 1.017

=0.165 percent

C) As shown above Rs 100 become 101.74 in 6 years as per the given returns. so $10,000 would have become $10,174 in 6 years (101.74*100)

D)

Taking the initial amount as 100 RS

we have amounts in the end of the year as

year 1= 180 year 2=90 year 3 =153 year 4=76.5 year 5= 107.1

Final year 6=101.74

Compound annual rate of return is (101.74/100)^1/6)-1=1.00165-1

=0.165 percent