Posted: March 3rd, 2025

Suppose the return on portfolio P has the following probability distribution

Problem 1
Suppose the return on portfolio P has the following
probability distribution:Bear
MarketNormal
marketBull
marketProbability0.20.50.3Return
on P-20%18%50%Assume that the risk-free rate is 9%, and the
expected return and standard deviation on the market portfolio M is 0.19 and
0.20, respectively. The correlation coefficient between portfolio P and the
market portfolio M is 0.6.
Answer the following questions:
1.
Is P efficient?2.
What is the beta of portfolio P?3.
What is the alpha of portfolio P? Is P
overpriced or underpriced?Problem 2
Consider a two factor
economy. Assume the risk-free rate = 3%, and the risk premiums are
RP1 = 10%, RP2 = 8%. The return on stock ABC is generated
according to the following equation:
rABC=0.08-0.55F1+1.2F2+eABC
Assume that the stock
is currently priced at $50 per share.
1.
What is the
expected return for stock ABC using the APT?2.
Is stock
ABC underpriced or overvalued?3.
If the
expected price next year will be $55, what is the stock price now that will not
allow for arbitrage profits?4.
Assume that
the risk free rate increases to 4%, with the other variables remaining
unchanged. Would you recommend to buy or
sell stock ABC?Problem 3
Suppose that the index model for two Canadian
stocks HD and ML is estimated with the following results:
RHD =0.02+0.80RM+eHD
R-squared =0.6
RML =-0.03+1.50RM+eML
R-squared =0.4
σM
=0.20
where M is S&P/TSX Comp Index, RX
is the excess return of stock X.
1.
What is the standard deviation of each
stock?2.
What is the systematic risk of each
stock?3.
What are the covariance and
correlation coefficient between HD and ML?4.
For portfolio P with investment
proportion of 0.3 in HD and 0.7 in ML, calculate the systematic risk,
non-systematic risk and total risk of P.Problem 4
Using the.finance.yahoo.com/">Yahoo! Finance website, search the Bank of Nova Scotia (BNS.TO)by finding
its stock symbol.If
you are unable to locate the prices for BNS.TO, use prices for BNS (the Bank of
Nova Scotia observed in US dollars at the New York Stock Exchange). For the
purpose of this question, assume that the Canadian dollar and the US dollar had
been exchanged one for one.Find historical prices for
the stock (on the left-hand menu) and complete the following:
1.
Download historical data for
the stock prices (adj. close) from January 1, 2004 through January 1, 2012, on
a monthly basis. You will also need to download
corresponding monthly prices for the S&P/TSX Comp index (also available on
the Yahoo! Finance site) as well as 3-month T-Bill rates (download this
attachment: .athabascau.ca/course/fnce401/v5and6/T-Bill%20Rates.xlsx">T-Bill
Rates.xlsx).2.
Calculate returns for both
series of prices downloaded from Yahoo site (BNS and S&P /TSX Comp Index). Prior
to that, make sure the data is sorted in ascending order (i.e., first row has
the oldest data). The final spreadsheet
should have the two series of returns you downloaded and calculated from Yahoo!
Finance. Make sure all data is expressed
in same units.3.
Using the Tools menu in EXCEL,
(Tool Pack has to be installed if EXCELdoes not show it) perform regression
analyses using the Market Model for BNS.4.
Clearly provide the regression
results in a table with an explanation for the coefficients obtained, and clear
interpretation. Specifically, for each regression provide:
·
Dependent Variable
·
Independent Variable
·
Intercept
·
Beta Value
·
Firm Specific Risk
i.
How well does the S&P/TSX Comp Index movement
explain the variability of the return on BNS stock?
ii.
What is the alpha of the BNS stock?
iii.
Calculate the standard deviation of the stock
return (using the equation for R2=β2σM2/σ2,and
the individual regression results).
iv.
Calculate systematic risk and firm specific risk
for the stock.Problem 3-1
Three years ago, you
purchased a bond for $974.69. The bond had three years to maturity, a coupon
rate of 8% paid annually, and a face value of $1,000. Each year you reinvested
all coupon interest at the prevailing reinvestment rate shown in the table below.
Today is the bond's maturity date. What is your realized compound yield on the
bond?TimePrevailing reinvestment rate0 (purchase date)6.0%17.2%29.4%3 (maturity date)Problem 3-2
You will be paying
$10,000 a year in education expenses at the end of the next two years.
Currently the yield curve is flat at 8%.
1.
If you want
to fully fund and immunize your obligation with a single issue of a zero-coupon
bond, what maturity bond must you purchase?2.
What must
be the market value and the face value of the zero-coupon bond?3.
Instead of
using a single zero-coupon bond, you prefer to use a one-year T-Bill and a
five-year zero-coupon bond to fund and immunize your obligation. How much of
each security will you buy?Problem 3-3
A
newly issued bond has the following characteristics:
Par value=$1000
Coupon rate =8%
Yield to Maturity = 8%
Time to maturity = 15 years
Duration =10 years1.
Calculate modified duration using the information above.2.
If the yield to maturity increases to 8.5%, what will be the
change (in dollar amount) in bond price?3.
Identify the direction of change in modified duration if:
i. the coupon of the bond is 4%, not 8%.
ii. the maturity of the bond is 7 years, not 15 years.
4.
How can you construct a portfolio with a duration of 8 years using
this bond and a 5 year zero coupon bond?Problem 3-4
You have been provided with the following
information zero coupon bonds with $1000 face value.Maturity - semi -annual periodssemi-annual spot rates14.2524.1533.9543.7053.5063.2573.0582.901.
Compute the forward interest
rates.2.
Graph the yield curve.3.
Explain the factors that account
for the shape of the curve.Problem 3-5
Company HTA had a free
cash flow for the firm (FCFF) of $1,500,000 last year. It is expected the FCFF
will keep a sustainable growth rate of 5%. The company has 2 million common
shares outstanding. In addition, the following information has been gathered:
Capital
structure: D/E=0.2:0.8；
Market
value of Debt: VD =$5,000,000;
Required
return on equity: kE =15%
Cost
of debt before tax =6%
Tax
rate: tc =25%;
Determine the fair
value of HTA stock.Problem 3-6
Company
JUK has a ROE of 25% and the company will not pay any dividend for the next 3
years. It is estimated that the company will pay $2 dividend per share after
three years and then to level off to 5% per year forever.
The
company has a beta of 2. Assume the risk-free interest rate is 4%, and the market
risk premium is 8%.
1.
What is your estimate of the fair price of a share of the stock?2.
If the market price of a share is equal to this intrinsic value,
what is the P/E ratio?3.
What do you expect its price to be 1 year from now? Is the implied
capital gain consistent with your estimate of the dividend yield and the market
capitalization rate?Problem 3-7
MicroSense, Inc., paid
$2 dividends per share last year. It is estimated that the company’s ROEs will
be 12% and 10%, respectively, next two years. The plowback rate in next two
years will be 0.6. It is expected that the dividends will grow at a sustainable
rate of 3% per year after two years. Assume that the expected return on the
market is 8%, the risk-free rate is 4%, and the beta of the stock is 1.4.What
is the fair price of the stock?Problem 3-8
An analyst uses the constant growth model
to evaluate a company with the following data for a company:
Leverage ratio
(asset/equity): 1.8
Total asset
turnover: 1.5
Current ratio: 1.8
Net profit margin: 8%
Dividend payout ratio:
40%
Earnings per share in
the past year: $0.85
The required rate
on equity: 15%
Based on an analysis, the growth rate of
the company will drop by 25 percent per year in the next two years and then keep
it afterward. Assume that the company
will keep its dividend policy unchanged.
1.
Determine the growth rate of
the company for each of next three years.2.
Use the multi-period DDM to estimate
the intrinsic value of the company’s stock.3.
Suppose after one year,
everything else will be unchanged but the required rate on equity will decrease
to 14%. What would be your holding period return for the year?Problem 4-1(15 marks)
The following information is given about options on the stock of a
certain company:
S0 = $20, X
=$20, r =5% (c.c.), T = 0.5 year,s= 0.20
No dividends are expected. One option contract is for 100 shares of
the stock. All notations are used in the same way as in the
Black-Scholes-Merton Model.
Answer the following questions:
1.
What is the European call
option price and European put option price, according to the Black-Scholes
model?2.
What is the cost of buying a
protective put?3.
What is the cost of writing a
covered call?4.
What will be the payoff and
profit of the protective put if the stock price on maturity is $16, $18, $20,
$22, or $24?Problem4-2
(15 marks)
A stock currently sells for $50. In six
months, it will either rise to $55 or decline to $45. The risk-free interest
rate is 6% per year.
1.
Find the value of a European
call option with an exercise price of $50.2.
Find the value of a European
put option with an exercise price of $50, using the binomial approach.3.
Verify the put-call parity
using the results of Questions 1 and 2.Problem
4-3 (15 marks)
An investor sold sevencontracts of June/2012 corn. The price per bushel was $1.64,
and each contract was for 5000 bushels.
The initial margin deposit is $2000 per contract with the maintenance
margin at $1250.
1.
How much did the investor have
to deposit on the investment?2.
The prices of the futures on
the four days following the short sales were 1.60, 1.66, 1.70, and 1.75.
Calculate the current balance on each of the next four days.3.
If the investor closed out her
position on the fifth day, what was her final gain or loss over the five days
in dollars and as a percentage of investment?4.
If the investor kept her
position, and the futures price on the sixth day was 1.80, would the investor
face a margin call? If yes, how much would she need to put up?Problem
4-4 (15 Marks)
Suppose the US dollar and Euro interest
rate for the next one year are 1.5% and 2%, respectively. Both are annually
compounded. The spot price of Euro is $1.3000, and the one-year forward price
of Euro is $1.2900. Determine the correct forward price and recommend an
arbitrage strategy.
Problem
4-5 (15 marks)The following data are available relating to the
performance of CSF Equity Fund and the market portfolio:Fund AFund BFund CMarket PortfolioAverage return18%12%30%15%Standard deviation25%15%30%20%Beta1.250.62.5The risk-free return during the sample period was 5%.
1.
Calculate
the performance measures of each of the funds (A, B, and C) using Sharpe's,
Treynor's, and Jensen's measures. Rank the results for each of the funds.2.
Identify
the fund(s) that outperformed the market using the Sharpe’s ratio and Treynor’s
measure, respectively.3.
Are the
rankings consistent? Explain any inconsistency.Problem4-6 (20 marks)The following performance information given
to you:Benchmark PortfolioJoe’s PortfolioKim’s PortfolioWeightReturnWeightReturnWeightReturnStocks0.6-5.00%Stocks0.5-4.00%Stocks0.3-5.00%Bonds0.33.50%Bonds0.22.50%Bonds0.43.50%T-Bills0.11.00%Cash0.31.00%Cash0.31.00%The risk-free rate is 1% and the standard deviation
for the Benchmark portfolio is 3.50%, Joe’s portfolio is 5.00% and Kim’s
portfolio is 3.00%.
1.
Compare Joe’s and Kim’s
performance relative to the benchmark in terms of portfolio returns.2.
If they are beating the market,
determine the sources of their success in terms of security selection and asset
allocation.
(a) Who is superior in security selection?
(b) Who is superior in asset allocation?
3.
Using Sharpe Index, determine
which manager is performing better than the market in a risk adjusted basis.

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