Question

F-I is the answers I need

Stock A and Stock B produced the following returns during the past five years (Year -1 is one year ago, Year -2 is two years ago, and so forth):

Year                            Stock A’s Returns,   Stock B’s Returns,

-1                                        –18.00%                                   –14.50%

-2                                          33.00                                         21.80

-3                                          15.00                                         30.50

-4                                          –0.50                                         –7.60

-5                                          27.00                                         26.30

1. Calculate the average rate of return for each stock during the past five years.
2. Assume that someone held a portfolio consisting of 50 percent Stock A and 50 percent Stock B. What would have been the realized rate of return on the portfolio in each year for the past five years? What would have been the average return on the portfolio during this period?
3. Calculate the standard deviation of returns for each stock and for the portfolio.
4. Calculate the coefficient of variation for each stock and for the portfolio. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?
5. Assume a third stock, Stock C, is available for inclusion in the portfolio. Stock C produced the following returns during the past five years:

Year                               Stock C’s Return, σ

-1                                            32.00%

-2                                          –11.75

-3                                            10.75

-4                                            32.25

-5                                            –6.75

Input these values and calculate the average return, standard deviation, and coefficient of variation for Stock C.

6. Assume that the portfolio now consists of 33.33 percent Stock A, 33.33 percent Stock B, and 33.34 percent Stock C. How does this composition affect the portfolio return, standard deviation, and coefficient of variation versus when 50 percent was invested in A and in B?
7. Make some other changes in the portfolio, making sure that the percentages sum to 100 percent. For example, enter 25 percent for Stock A, 25 percent for Stock B, and 50 percent for Stock C. Notice that remains constant and that s_p changes. Why do these results occur?
8. In part b, you should see that the standard deviation of the portfolio decreased only slightly because Stocks A and B were highly positively correlated with each other. The addition of Stock C causes the standard deviation of the portfolio to decline dramatically, even though s_C = s_A = s_B. What does this change indicate about the correlation between Stock C and Stocks A and B?
1. Would you prefer to hold a portfolio consisting only of Stocks A and B or a portfolio that also includes Stock C? If others react similarly, how might this fact affect the stocks’ prices and rates of return?

Answer 1

a) Average rate of return for the past 5 years = Sum of Returns/ 5

Therefore, Average return of A = (-18+33+15-0.5+27) / 5 = 11.30%

Therefore, Average return of B = (-14.5+21.8+30.5-7.6+26.30) / 5 = 11.30%

b) If someone had 50% stock A and 50% stock B in their portfolio, then every year the returns would be

For year -1 , the return would be (-18%+ (-14.5%))/2 = -16.25%

For year -2 , the return would be (33%+ 21.8%)/2 = 27.4%

For year -3 , the return would be (15%+ 30.5%)/2 = 22.75%

For year -4 , the return would be (-0.5%+ (-7.6%))/2 = -4.05%

For year -5 , the return would be (27%+ 26.30%)/2 = 26.65%

The Average return on the portfolio = (-16.25+27.4+22.75-4.05+26.65)/5 = 11.30%

c) Standard Deviation is calculated by

where Ri is the Return in period i and is the average return

So Standard Deviation (A) = sqrt {[{ (-18 -11.30)² + (33-11.30)²+(15-11.30)²+(-0.5-11.30)²+(27-11.30)²}/4]

=sqrt [{(-29.30)² + 21.7² +3.7² + (-11.8)² + 15.7²}/4]

=20.79%

& Standard Deviation (B) = sqrt {[{ (-14.5 -11.30)² + (21.8-11.30)²+(30.5-11.30)²+(-7.6-11.30)²+(26.30-11.30)²}/4]

=sqrt [{(-25.80)² + 10.5² +19.20² + (-18.9)² + 15²}/4]

=20.78%

& Standard Deviation (portfolio) = sqrt {[{ (-16.25 -11.30)² + (27.4-11.30)²+(22.75-11.30)²+(-4.05-11.30)²+(26.65-11.30)²}/4]

   =20.13%

d) CV (A) = standard Deviation (A) / Average return of A

= 20.79%/11.3% = 1.8398

CV (B) = 20.78%/11.3% = 1.8387

& CV(port) = 20.13%/11.30% = 1.7812

If I am a risk averse investor, I would prefer the portfolio over A or B because of lower Coefficient of Variation (CV)