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Solution_Worsksheet_Chapter11_FIN 332

 

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  1. Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $56. The stock will pay a dividend at year-end of $4.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.9%.

 

Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2015 (figures in percent per year) are as follows.

 

Portfolio Average Annual
Rate of Return (%)		 Average Premium (Extra return
versus Treasury bills) (%)
Treasury bills   3.8        
Treasury bonds   5.3     1.5  
Common stocks   11.4     7.6  

 

  1. What is the discount rate on the stock?

Hint: discount rate is the rate of return.

 

 

  1. What price should she be willing to pay for the stock today?

 

Hint: Current stock price is the present value of the expected cash flows.  Or ,you can use rate of return formula.


 

 

  1. Assume these are the stock market and Treasury bill returns for a 5-year period:

 

Year   Stock Market Return (%) T-Bill Return (%)
2011     −36.43     2.40  
2012     29.20     0.80  
2013     16.36     0.17  
2014     1.68     0.09  
2015     17.16     0.11  

 

  1. What was the risk premium on common stock in each year? .)

 

 

  1. What was the average risk premium?

 

 

 

  1. What was the standard deviation of the risk premium?

 

 

Hint_Solution:

a.

 

Year Stock Market Return T-Bill Return   Risk Premium   Deviation from Mean   Squared Deviation  
2011   –0.3643     0.0240       -0.3883       –0.4371       0.1911    
2012                                      
2013                                      
2014                                      
2015                                      
        Average risk premium                    
                    Variance      
                          Standard deviation      

 

b.

The average risk premium was

 

c.

The variance (the average squared deviation from the mean) was

 

Therefore: Standard deviation = 23.45%.

 

 

  1. A stock is selling today for $60 per share. At the end of the year, it pays a dividend of $3 per share and sells for $66.

 

  1. What is the total rate of return on the stock?

 

 

  1. What are the dividend yield and percentage capital gain?

 

 

  1. Now suppose the year-end stock price after the dividend is paid is $51. What are the dividend yield and percentage capital gain in this case?

 

 

  1. Is there any change in the dividend yield calculated in parts (b) and (c)?

 

 

Hint_Solution:

 

a.

Total percentage return = (Capital gain + Dividend) / Initial share price
     
     

 

b.

 
Dividend yield = Dividend / Initial share price
  =  
  =  

 

   
Capital gains yield = Capital gain / Initial share price
  =
  =

 

c.

 

Dividend yield = Dividend / Initial share price
  =
  =

 

Capital gains yield = Capital gain / Initial share price
  =
  =

 

d.

The dividend yield is unaffected by the ending share price because the yield is based on the initial price.

 

 

  1. Consider the following scenario analysis:

 

    Rate of Return
Scenario Probability Stocks Bonds
Recession 0.20 –5 % 19 %
Normal economy 0.70 20   10  
Boom 0.10 32   9  

 

  1. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

Yes or No , why ?

 

  1. Calculate the expected rate of return and standard deviation for each investment

 

 

Hint_Solution:

 

a.

Interest rates tend to fall at the outset of a recession and rise during boom periods. Because bond prices move inversely with interest rates, bonds provide higher returns during recessions when interest rates fall.

 

b.

rstock = [0.2 × (−5%)] + (0.7 × 20%) + (0.1 × 32%) = 16.2%

 

rbonds =

 

Variance (stocks) =

 

Standard deviation =

 

Variance (bonds) =

 

Standard deviation = 13.411/2 = 3.66%

 

Stocks have both higher expected return and higher volatility. More risk-averse investors will choose bonds, while those who are less risk-averse might choose stocks.

Hint #1

 

 

  1. Here are the returns on two stocks.

 

    Digital Cheese Executive Fruit
January     +16     +9  
February     −2     +1  
March     +4     +3  
April     +6     +14  
May     −5     +3  
June     +2     +6  
July     −1     −2  
August     −7     −1  

 

  1. Calculate the variance and standard deviation of each stock. Which stock is the riskier if held on its own?

 

 

 

  1. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.

 

 

  1. Is the standard deviation more or less than halfway between the variance of the two individual stocks?

 

rev: 04_18_2018_QC_CS-124792, 05_01_2018_QC_CS-125920

 

 

Hint_Solution:

a.

The calculation of risk is in the following tables. Digital Cheese carries more risk with a standard deviation of 6.80 versus 5.00 for Executive Fruit:

 

  Digital
Cheese
Return		   Deviation
From
Mean		   Squared
Deviation
From Mean		     Executive
Fruit
Return		   Deviation
From
Mean		   Squared
Deviation
From Mean
January   16.00       14.38       206.64     January   9.00       4.88       23.77  
February                         February                      
March                         March                      
April                         April                      
May                         May                      
June                         June                      
July                         July                      
August                         August                      
Ave Return                 369.88     Ave Return                    
Variance                         Variance                      
stnd.dev.                         stnd.dev.   5.01                  

 

b.

The portfolio returns and variance are calculated as follows:

 

  Digital
Cheese
Return		   Executive
Fruit
Return		   50/50
Portfolio
Return		   Deviation
From
Mean		   Squared
Deviation
From Mean		  
January   16.00       9.00       12.50       9.62       92.64    
February                                        
March                                        
April                                        
May                                        
June                                        
July                                        
August                                        
          Ave Return                            
          Variance                            
          stnd.dev.       5.45                    

 

c.

The portfolio standard deviation is 5.5, which is less than the average of 5.9.

 

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