Suggested Solutions to Sample Midterm #1
Fi 4000—Fall 2014
Problem 1(20 points)
Suppose Robert wants to prepare an amount of money today to compliment his boy's college education. He desires his son to enter a school in 16 years with annual tuition and expenses of $25, 000 pertaining to 4 years. His initial college tuition and expenses will certainly due in exactly sixteen years coming from now. Mike decides to put all the money that is required pertaining to his boy's college education today at a bank account earning level of return of almost eight percent per year, compounded annually. How much money need to Mike set aside today? (10 points)
We could calculate the modern day value from the tuition payments as a reduced annuity:
Remember that we low cost the premium by 15 periods since the first payment is in 12 months 16.
Suppose that, instead of preparing a lump sum today, Mike will pay in a fixed sum of money every year for 12 years inside the same savings account. The 1st deposit will begin at the end of the year. Just how much amount must he pay in per year? (10 points)
Seek out an pension that will be comparable to $26, 103. 01 in present worth. Let T be the unknown volume of fixed annual savings.
Problem 2 (30 points)
Consider the subsequent two shares.
Stock BBT has an predicted return of 19% and a standard deviation of 23%. Stock DIS has an expected return of 13% and standard change of 17%. The relationship coefficient involving the returns of the two stocks and options is 0. 3. The danger free price of go back is 8%.
A buyer constructs a great optimal risky portfolio while using two shares BBT and DIS. Allow the optimal portfolio weights of DIS and BBT in the risky stock portfolio be forty percent and 60%, respectively.
The investor determines to construct an entire portfolio together with the optimal dangerous portfolio and risk free asset and makes a decision to set aside 35% of the total expenditure in risk free asset and 65% in the total investment in the dangerous portfolio.
A. Compute the expected returning of the optimum risky stock portfolio. (6 points)
B. Figure out the standard deviation of the optimum risky profile. (6 points)
C. Calculate the reward-to-variability ratio in the optimal high-risk portfolio. (6 points)
Reward-to-variability ratio sama dengan
M. Compute the fraction of the total portfolio C that is used stock DIS and the cheaper complete profile that is committed to BBT. (6 points)
Allow y =0. 65 be the cheaper complete profile invested in the risky portfolio Let 1-y = 0. 35 be the cheaper complete portfolio invested in the riskfree advantage.
fraction of C invested in DIS = zero. 65 (0. 40) = 0. 26
fraction of C committed to BBT sama dengan 0. 65(0. 6) sama dengan 0. 39
E. Calculate the anticipated return from the complete portfolio C. (6 points)
Problem 3 (20 points)
Suppose that the CAPM is a valid description of security results over the following 12 months and also you, being a financial analyst, will be analyzing some securities. You could have the following info:
a. Write down an equation that relates the expected come back of a stock X, Electronic[rX], to its systematic risk. (5 points)
w. What is the expected go back of Times if X's beta is definitely 1 . 5? (5 points)
c. Is it possible to have a stock A with expected come back of 10% and common deviation of 20%? So why or why not? (5 points)
For the industry, the reward-to-variability ratio is (0. 12-0. 06)/0. 18 = zero. 33. Share A could have a reward-to-variability ratio of (0. 10-0. 06)/0. 20 = 0. 20.
Thus, A is much less efficient compared to the market, which can be possible inside the CAPM.
g. Is it possible to have got a stock W with anticipated return of 18% and standard change of 24%? Why or perhaps why not? (5 points) As before, the market has a reward-to-variability ratio of 0. thirty-three. Stock M would have a reward-to-variability proportion of (0. 18-0. 06)/0. 24 = 0. your five.
Thus, Stock B would be on a higher CAL than the market. This is simply not possible considering that the CAPM says that...