Tyler Trucks stock has an annual return mean and standard deviation of 10 percen

Question

Tyler Trucks stock has an annual return mean and standard deviation of 10 percent and 39 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 11.6 percent and 45 percent, respectively. Your portfolio allocates equal funds to Tyler Trucks stock and Michael Moped Manufacturing stock. The return correlation between Tyler Trucks and Michael Moped Manufacturing is .5. What is the smallest expected loss for your portfolio in the coming month with a probability of 2.5 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.)

Tyler Trucks stock has an annual return mean and standard deviation of 10 percent and 39 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 11.6 percent and 45 percent, respectively. Your portfolio allocates equal funds to Tyler Trucks stock and Michael Moped Manufacturing stock. The return correlation between Tyler Trucks and Michael Moped Manufacturing is .5. What is the smallest expected loss for your portfolio in the coming month with a probability of 2.5 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.)

Explanation / Answer

Given

Tyler trucker, mean=10, ?t= 39%

Michel moped, mean=11.6, ?m = 45%

Correlation of coefficient (?) =0.5, weights = 0.5 each

Smallest expected loss (VAR) Value at risk =?

In VAR there is a variance covariance method that can be used to find minimum expected loss with 2.5 %

This means there is 97.5 % confidence level the value at this point the normal distribution Value is2.24

First calculate portfolio risk

= ?wt2 ?t2 +wm2 ?m2 + 2 ? wt wm ?t ?m

?0.52 *0.392 + 0.52* 0.452+ 2 * 0.5*0.5*0.5*0.39*0.45

=?0.424

Standard deviation of a portfolio ( ?) =0.6512

Now find the value at risk (VAR) the minimum expected loss with 2.5 %

VAR = standard deviation of a portfolio * -2.24 ( as it a loss )

VAR = -2.24 * 0.6152

VAR = -1.378

The minimum expected loss on a portfolio is 1.378

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