Question

Stocks for Fumbeshi and Mundashi have the following historical returns: Table 2 Year Fumbeshi Mundashi 2010 -18% -14.5% 2011 33% 21.8% 2012 15% 30.5% 2013 -0.5% -7.6% 2015 27% 26.3% (i) What is the average return rate of return for each stock during the period 2010 through 2015? (ii) Assuming someone held a portfolio consisting of 50 percent of stocks Fumbeshi and 50 percent stocks of Mundashi, what would have been the realized return on the portfolio during this period? (iii) What is the standard deviation of each stock during the period 2010 through 2015? (iv) Which of the stocks Fumbeshi or Mundashi performed better in terms of both the risk and return? (Hint: Back your answer with computations) Total

Answer 1

Ans:- (i)

years	Fumbeshi	Mundashi
2010	-18%	-14.5%
2011	33%	21.8%
2012	15%	30.5%
2013	-0.5%	-7.6%
2015	27%	26.3%
Total	56.5%	56.5%

Average rate of return for Fumbeshi stocks will be given by (Total return / 5 ) = 56.5% / 5 = 11.3%

Average rate of return for Mundashi Stocks will be given by ( Total return / 5 ) = 56.5% / 5 = 11.3%

(ii) If someone held portfolio constisting of 50 percent of stocks in Fumbeshi and 50 percent stocks in Mundashi, then the realized return on the portfolio will be given by

0.50 * 11.3 + 0.50 * 11.3 = 11.3% is the realized on the portfolio during this period.

(iii) calculating standard deviation for stock Fumbeshi

Fumbeshi	Deviation	Deviation^2
-18%	-18-11.3 = -29.3	858.49
33%	33 - 11.3 = 21.7	470.89
15%	15 - 11.3 =3.7	13.69
-0.5%	-0.5 -11.3 = -11.8	139.24
27%	27 - 11.3 =15.7	246.49
Total		1728.8

Note:- Deviation is nothing but the (return - average return on the stock)

Variance = (Sum of deviation^2/ n-1)

= (1728.8/5-1) =432.2

Now SD is nothing but the square root of variance i.e 432.2

SD = 20.78.

Calculating SD for stock Mundashi.

Mundashi	Deviation	Deviation^2
-14.5%	-14.5-11.3 =-25.8	665.64
21.8%	21.8-11.3=10.5	110.25
30.5%	30.5-11.3=19.2	368.64
-7.6%	-7.6-11.3=-18.9	357.21
26.3%	26.3-11.3 =15	225
Total		1726.24

Variance = 1726.244/5-1 = 431.685

SD is the square root of variance i.e 431.685

SD = 20.77

(iv) we know that SD is nothing but the total risk of the stock i.e systematic risk and unsystematic risk the more is the SD more is the risk associated with the stock. Since the return on both the stocks is the same i.e 11.3% but the SD of Fumbeshi is slightly high, therefore it is better to invest in Mundashi because the return will be the same with lower risk. Therefore the Mundashi stock is slightly better as compared to Fumbeshi.

Note:- Return in both the stocks is the same with approximately the same risks but Fumbeshi stock has a slight advantage, therefore, the answer for part (iv) can also be both the stocks has the same return with approximately the same.so choose your answer as per your book and convenience.

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