Question

Investment B is represented by the cash value of a whole life insurance policy. 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

+4.9%

2

+5.0%

3

+4.6%

4

+5.1%

5

+4.9%

6

+4.8%

9. 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 B over the 6-year period? ___________

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

Investment C is an equity (stock) investment in a British 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

+70%

2

-45%

3

+80%

4

-42%

5

+50%

6

-8%

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

12. What is the expected average annual rate of return on Investment C? ___________

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

Answer 1

9) Let us assume the initial investment is 100

So amount after 6 years is =Investment (1+retun)

=100(1.049)*1.05*1.046*1.051*1.049*1.048=133.12

So annual compounded return calculation is

Future value= present value (1+return)^ Period

133.12=100(1+i)^6

1.332=(1+i)^6

1+i=(1.332)^(1/6)

Annual compounded rate of return =4.88%

10) Let us calculate the standard deviation of the return

Year	Return (X)	(X-mean)^2
1	4.90%	0.00000%
2	5.00%	0.00014%
3	4.60%	0.00080%
4	5.10%	0.00047%
5	4.90%	0.00000%
6	4.80%	0.00007%
Total	29.3%	0.001%

Average= Sum of return/Number of years=29.3%/6=4.88%

Standard deviation=(Sum (X-mean)^2/N)^(1/2)

=(0.001%/6)^(1/2)=0.16%

Now rate of return per unit of risks=Return/Risk=4.88%/0.16%=31.06 times

11) Calculation of standard deviation

Year	Return (X)	(X-mean)^2
1	70%	28%
2	(45%)	39%
3	80%	39%
4	(42%)	35%
5	50%	11%
6	(8%)	7%
Total	105%	158%

Mean=Total return/Period=105%/6=15.50%

Standard deviation=(Sum (X-mean)^2/N)^(1/2)

=(158%/6)^(1/2)=51.34%

12) Expected average rate of return=15.50%

13) Investment after 6 years for initial investment of 10,000 is

Future value==Investment (1+retun)

=10,000(1+.7)*(1-0.45)*(1+.8)*(1-.42)*(1+0.5)*(1-0.08)= 13,470