FNCE3000 - Mortgage Payments - Market Risk Premium - Portfolio Expected Return and Historical Volatility - Finance Assessment Answer

Assessment Task:

FNCE3000 Mortgage Payments Finance Assessment Answer

Task Description:

You want to buy a $1,000,000 house. Suppose you make a 20% down payment today, and you finance the rest of your purchase with a 30?year fixed-rate jumbo mortgage.

1) What will be your monthly mortgage payments?

2) How much of your first month’s payment goes toward paying off interest? How much goes toward paying off the loan balance?

3) How much do you still owe after 5 years (i.e., just after your 60th monthly payment)?

4) How long will it take you to reduce your loan balance by half (i.e., ≤ $400,000)? 5) Suppose in 20 years (just after your 240th monthly payment), you decide to refinance at a 10?year fixed rate of 3.200%. What will be your new monthly mortgage payments?

In your calculations below, assume that the annual risk?free rate is rf=2%.

Part 1: Estimate the Market Risk Premium

Estimate the (annual) market risk premium using the five?year time series of monthly pricing data from October 2012 through October 2017 (inclusive). Use the S&P500 Composite Index as your proxy for the “market” (in the “Get Quotes” box type “^GSPC”).

The monthly closing prices are provided under the “historical prices” tab. From here, you can calculate monthly stock returns. The prices reported here are adjusted prices—which means stock splits and dividend payments have already been factored in such that you need only to calculate the percentage change in these ‘adjusted’ prices to derive the stock returns.

Part 2: Calculate Portfolio Expected Return and Historical Volatility

Suppose you invest half of your wealth in MSFT and the other half in KO.

1. Assuming that CAPM holds, what is the annual expected return on your portfolio?

Based on the five?year period spanning October 2012 through October 2017…

2. What is the annualized historical volatility of your portfolio returns?

3. What is the annualized average return?

4. What is the realized return on your investment if you purchased this portfolio on the first trading day of October 2012 and sold it on the last trading day of October 2017?

Part 3: Calculate Betas

Try estimating beta yourself (for both MSFT and KO) using the five?year time series of monthly stock returns from October 2012 through October 2017 (inclusive).

Recall that a stock’s beta is calculated as: the covariance between its excess returns and excess market returns (for simplicity, you can just use S&P 500 index returns), divided by the variance of excess market returns—i.e., Cov(rM,ri)/var(rM). (‘excess return’ refers to the return in excess of the riskless rate).

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