Question

Please answer All, I do not have computer to solve. Thank you !

1. You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to medical school is about 20 percent. If you are accepted to medical school, then your starting salary when you graduate will be $320,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $46,000 per year. Without considering the additional years you would spend in school if you study medicine or the time value of money.

- Expected starting salary:

-Standard deviation:

2. Stocks A, B, and C have expected returns of 14 percent, 14 percent, and 10 percent, respectively, while their standard deviations are 49 percent, 21 percent, and 21 percent, respectively. If you were considering the purchase of each of these stocks as the only holding in your portfolio and the risk-free rate is 0 percent, which stock should you choose?

Coefficient of variation for stock

-A:

-B:

-C:

3. David invested $1,000 in large U.S. stocks at the beginning of 2012. This investment earned 15.30 percent in 2012, 31.50 percent in 2013, 13.50 percent in 2014, and 2.30 percent in 2015. What return did he earn in the average year during the 2012–2015 period?

-Returned earned in the average year: %

4. Michael invested $1,000 in large U.S. stocks at the beginning of 2012. This investment earned 17.35 percent in 2012, 30.95 percent in 2013, 11.45 percent in 2014, and 1.60 percent in 2015. What was the average annual return that Michael earned over the 2012–2015 period.

-Average annual return earned3

5.Assume the expected return on the market is 10 percent and the risk-free rate is 4 percent, What is the expected return for a stock with a beta equal to 2.00? What is the market risk premium?

-Expected return:

-market risk premium:

6.Linda is considering investing in a company's stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment.

		Probability		Return
Boom		0.4		25.00%
Good		0.2		15.00%
Level		0.2		10.00%
Slump		0.2		-5.00%

-expected return on Linda’s investment:

- determine the standard deviation of the return on Linda's investment:

Answer 1

1) Expected Value Formula:

E(X) = ∑X * P(X) where X is the value associated with an event and P(X) is the probability of the occurrence of the event.

Thus, Expected Starting Salary= 320000*0.2 + 46000*(1-.20)= 64000 + 36800 = 100800

2) Coefficient of Variation (CV) Formula:

where σ is the standard deviation and μ is the mean

CV for stock= Standard Deviation of return of stock/ Mean Expected Return

CV for A= 49/14 = 3.5

CV for B= 21/14= 1.5

CV for C= 21/10= 2.1

3) Return earned in the average year= Arithmetic Mean of returns = Sum of all returns/ No. of years

= (15.3+31.5+13.5+2.3)/4 = 15.65%

4) Formula for Annualised Average Return YoY: Geometric mean of returns

where r is the return and n is the number of years

= ((1+0.1735)*(1+0.3095)*(1+0.1145)*(1+0.016))^1/4 -1 = 1.15-1 = 0.15 or 15%

5) Expected Return on Security using CAPM method:

E(R)= Risk Free Rate + Beta*(Market Risk- Risk Free Rate)

E(R)= 4% + 2*(10%-4%) = 16%

Market Risk Premium= Market Risk- Risk Free Rate= 6%

6) E(R) = ∑R* P(R) where R is the return in a particular event and P is the probability associated with the event

= 25%*0.4 + 15%*0.2 + 10%*0.2 + (-5%)*0.2 = 0.14 or 14%

Standard Deviation of Returns (Sigma) :

where r_i is the rate of return in the ith outcome, ERR is the expected rate of return or mean return, p_i is the probability of ith outcome, and n is the number of possible outcomes.

Std Deviation= [ (0.25-0.14)²*0.4 + (0.15-0.14)²*0.2 + (0.10-0.14)²*0.2 + (-0.05-0.14)²*0.2 ]^1/2 = (0.01240)^1/2

=0.11136 or 11.14%