Formulas:
Percentage return=(capital gain+dividend)/(initial share price)
Dividend yield=dividend/(initial share price)
Capital gain yield=(capital gain)/(initial share price)
1+real rate of return=(1+nominal rate of return)/(1+inflation rate)
Variance=average of squared deviations around the average
Standard deviation=square root of variance
Portfolio rate of return=(fraction of portfolio in first assetrate of return on first asset)+(fraction of portfolio in second assetrate of return on second asset)

Questions:
Provide an answer, example, or explanation for the following items:
Provide an example of systematic risk

Provide an example of unsystematic risk 






Explain the risk premium for investments 





Explain why someone might be willing to invest in treasuries, given that the average return to treasuries has been lower than that of equities.  





Which would likely provide greater diversification benefits, adding a third stock to a portfolio of two, or adding a 50th stock to a portfolio of 49? Why? 





Explain why adding international equities might offer diversification benefits relative to a purely domestic portfolio.  





Consider a stock’s percentage return. A stock is selling on January 1 for $40/share. At the end of the year, it pays a dividend of $2/share and sells for $44. 
What is the total rate of return on the stock? 




What are the dividend yield and capital gain yield? 




Now suppose the year-end stock price, after the $2 dividend is paid, is $36. What are the percentage return, the dividend yield, and the capital gain yield in this case? 




Consider the expected return formula and calculation. 
An asset will return either 10% with probability 0.3 or 20% with probability 0.7. What is the expected return? 
There is a 0.3 probability that a bond will default. In the event of default, the bond will be worth $25. If the bond does not default (probability = 1-0.3=0.7) then it will be worth $100. The bond is currently trading for $90. What is the expected return? 






A bond investor is considering an investment. The investor believes that there is a 10% chance that the bond will completely default and be worth zero. There is a 90% chance that the bond will return its full par value of $100. Given this risk, the investor requires an 8% expected rate of return. How much will the bond investor be willing to pay for the bond today?  






Explain what would happen to the bond price if the investor required a greater or lower expected rate of return.  



An entrepreneur is requesting a loan of $100 today. The bank forecasts that the startup has a 20% chance of failure, in which the venture would be worth only $50 in salvage value. The bank also forecasts that there is an 80% chance of success in which case the venture would be worth $500. The bank requires a 10% expected rate of return in order to offer the loan. How much must the entrepreneur promise to repay in the good state (success) such that the bank may realize the expected return? 





What would happen to the promised repayment if the probability of failure increased? 



The common stock of Leaning Tower of Pita, a restaurant chain, will generate payoffs to investors next year, which depend on the state of the economy, as follows: an $8 dividend and $240 stock price in the event of a boom, a $4 dividend and $90 stock price in the event of a normal economy, and no dividend and a $0 stock price in the event of a recession. Assume all states are equally likely. The stock is selling for $80 today. What is the expected return and standard deviation of the return to the shareholders? 











The common stock of Escapist Films sells for $25/share and offers the following payoffs next year: $0 dividend and $18 stock price in a boom, $1 dividend and $26 stock price in a normal economy, and a $3 dividend and $34 stock price in the event of a recession. 
Calculate the expected return and standard deviation 

Calculate the expected return and standard deviation of a portfolio that is invested equally in both Escapist Films and Leaning Tower of Pita.

Sample Solution