Assignment

You have $30,000 in your margin account, and you want to invest in BMO stock. The minimum margin requirement for BMO is 30%. You just got a quote on BMO as follows:

Bid: 55.25

Ask: 55.26

The interest rate on the margin loan is 6% per annum.

1) If you want to buy BMO in margin, what is the maximum number of shares can you buy?

2) Suppose you want to buy 1200 shares of BMO in margin. Answer the following questions:

a. What is the initial margin ratio?

b. Suppose you are going to hold the shares for one year. At what price at the end of next year will your investment break even? (assuming no margin calls in the year)

c. How far could the stock price fall before getting a margin call?

d. If the stock price falls to $40, you would get a margin call. If this happens, how much new fund would you need to add to your account to respond the margin call?

SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used as proxies for the US and Canadian stock markets, respectively. From a set of their historical data, the annual expected returns and standard deviations of those two ETFs and their covariance are estimated as follows:

SPY: E(r) = 0.36 σ=0.26 XIU: E(r) = 0.44 σ=0.28 Covariance between= 0.0568

Suppose that you have $5 million to invest for one year and you want to invest this money into SPY, XIU and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-Bill is 6% per annum.

Suppose that you have the following utility function:

U=E(r) - σ2

Answer following questions using EXCEL:

1) Draw the opportunity set offered by these two securities (with an increment of 0.01 in weight).

2) What is the optimal portfolio of SPY and XIU?

3) Determine your optimal asset allocation among SPY, XIU, and T-Bill, in percentage and in dollar amounts.

Using the 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: 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 EXCEL does 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.