Question

Below are the holding period returns for the past five years for Microsoft (MSFT) and the S&P 500

Date MSFT S&500

2017 15% 8%

2016 7% 9%

2015 25% 12%

2014 15% 7%

2013 6% 5%

a. Calculate the average arithmetic return and standard deviation for MSFT and the S&P500.

b. Assuming you are a risk averse investor and expect the next 12 months to be similar to the past twelve months. If you had to make a choice between investing in either MSFT or the S&P 500 which one would you choose? Why?

c. Assuming you could hold 50% of your funds in each security would this change your decision? (please calculate the average return and standard deviation of the equally weighted portfolio – assume a correlation coefficient of .5).

Answer 1

a. Calculation of average arithmetic return and standard deviation for MSFT and the S&P500.

average arithmetic return = sum of returns / no. of returns

average arithmetic return for MSFT = (15+7+25+15+6) / 5

= 68 / 5

= 13.60%

average arithmetic return for S&P 500 = (8+9+12+7+5) / 5

= 41 / 5

= 8.20%

-standard deviation for MSFT

Year	Return(%)	Deviation from expected return of 13.60(D1)	D12
2013	6.00	-7.60	57.76
2014	15.00	1.40	1.96
2015	25.00	11.40	129.96
2016	7.00	-6.60	43.56
2017	15.00	1.40	1.96

Variance = D1² / n

= (57.76+1.96+129.96+43.56+1.96) / 5

= 235.20 / 5

= 47.04

Standard Deviation = Variance

= 47.04

= 6.86%

-standard deviation for S&P500

Year	Return(%)	Deviation from expected return of 8.20(D2)	D22
2013	5.00	-3.20	10.24
2014	7.00	-1.20	1.44
2015	12.00	3.80	14.44
2016	9.00	0.80	0.64
2017	8.00	-0.20	0.04

Variance = D2² / n

= (10.24+1.44+14.44+.64+.04) / 5

= 26.80 / 5

= 5.36

Standard Deviation = Variance

= 5.36

= 2.32%

b) Risk averse investor also called as Conservative investor were more concentrate on Risk. Out of two stocks of similar expected return, they will select one which has the lower risk. In the given case, MSFT and S&P500 have an expected return of 15% and 8% respectively and have a standard deviation of 6.86% and 2.32% respectively. Hence a risk averse investor will choose S&P500 since it has lower risk.

c) calculate the average return and standard deviation of the equally weighted portfolio

-average return of the equally weighted portfolio

The return of a portfolio is the weighted average return of the securities which constitute the porfolio.

Security	Weight	Expected Return (%)	Weight*Expected Return
MSFT	0.50	13.60	6.80
S&P500	0.50	8.20	4.10

Portfolio Return = 10.90% (6.8+4.1)

-standard deviation of the equally weighted portfolio

(WA*SDA)² + (WB*SDB)² + (2*WA*WB*SDA*SDB*CorAB)

where

WA - Weight of MSFT

SDA - Standard Deviation of MSFt

WA - Weight of S&P500

SDA - Standard Deviation of S&P500

CorAB - correlation coefficient

(.5*.0686)² + (.5*.0232)² + (2*.5*.5*.0686*.0232*.5)

0.001709

.0413

4.13%

Now portfolio and S&P500 have an expected return of 10.90% and 8% respectively and have a standard deviation of 4.13% and 2.32% respectively. Hence a risk averse investor still choose S&P500 since it has lower risk.