Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. s

ID: 2717264 • Letter: Y

Question

Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. stock has an annual return mean and standard deviation of 11 percent and 34 percent, respectively. Woodpecker, Inc., stock has an annual return mean and standard deviation of 22 percent and 48 percent, respectively. The return correlation between DW Co. and Woodpecker, Inc., is zero. What is the smallest expected loss for your portfolio in the coming month with a probability of 5 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Woodpecker, Inc., stock has an annual return mean and standard deviation of 12.6 percent and 44 percent, respectively. What is the smallest expected loss in the coming month with a probability of 16.0 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Smallest expected loss %

Explanation / Answer

Answer to Part I

DW Co

Mean Return = 11%

Standard Deviation = 34%

Woodpecker Inc

Mean Return = 22%

Standard Deviation = 48%

Period of return calculation = 12 months

Coefficient of Correlation between DW Co and Woodpecker Inc = 0

Weights of stocks in portfolio

Woodpecker = DW Co = 0.5

Expected return on the portfolio = 0.5 * 11% + 0.5 * 22% = 5.5% + 11% = 16.5%

Correlation Coefficient = 0

Correlation Coefficient = Covariance (x, y)/(Standard deviation of X * Standard Deviation of y)

0 = Covariance / (034 * 0.48)

0 = Covariance / 0.1632

Covariance = 0* 0.1632 = 0

Variance of the portfolio = w1^2 * Standard Deviation^2 +w2^2 * Standard Deviation 2^2 + 2*w1*w2*Covariance

Variance of Portfolio = 0.5^2 * 0.34^2 + 0.5^2 *0.48^2 + 2 * 0.5*0.5 * 0

Variance of Portfolio = 0.25 * 0.1156 + 0.25 * 0.2304

Variance of Portfolio = 0.0289 + 0.0576

Variance of Portfolio = 0.0865

Standard Deviation of Portfolio = Square root (Variance) = Square root (0.0865) = 0.294108

Standard Deviation of Portfolio = 29.41% (rounded off)

Assuming that the returns on portfolio form a normal distribution, probability of 5% is -1.67 standard deviations away from mean which indicates negative returns.

Smallest expected loss next month = -1.65 * Standard Deviation * Square root of (Time) + Mean Return

Smallest Expected Loss next month = -1.65 * 0.2941 * Sqare root(12 months) + 0.165

= -1.681007 + 0.165 = - 1.5160072 or -151.60% (rounded off)

Asnwer to Part II

Annual mean return = 12.6%

Standard Deviation = 44%

Period of return calculation = 12 months

Probability for smallest loss = 16%

Confidence level of profitability = 100-16% = 84%

In a normal distribution confidence level of 68% is 1 standard deviation away from mean while 95% confidence level is 1.65 standard deviations away from the mean. Hence an 84% confidence level will be

Distance from Mean = -1 standard deviation - (84-68)/(95-68) =-1 standard deviation - 16/27

= -1 standard deviation - 0.5925 standard deviations

= -1.59 standard deviations

Smallest expected loss in next month = - 1.59 * 0.44 * Square root(12 months) + 0.126

= -2.42349 + 0.126 = -2.297485 or -229.75%

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Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. s

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Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. s

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