Please answer this 6 long questions below with the correct answer. If I could have this by tomorrow I would like to tip for a job well done, thanks.

1.Suppose that a two-factor model, where the factors are the market return (Factor 1) and the growth rate of industrial production (Factor 2), correctly describes the return generating processes of all assets and the corresponding two-factor APT correctly prices three well-diversified portfolios, A, B, and C.

Portfolio

Expected Return

Sensitivity to Factor 1

Sensitivity to Factor 2

A

15%

1

0

B

20%

1

1

C

5%

0

0

a.What are i) the risk premiums of the two factors and ii) the risk-free rate?

(4 marks)

b.Another well-diversified portfolio D has sensitivities 0 and 1 to factor 1 and factor 2, respectively. What is the APT-consistent expected return on Portfolio D?

(2 marks)

c.Suppose that Portfolio D's expected return is 8%. Given your answers above, design an arbitrage strategy involving Portfolios A, B, C, and D. (Hint: an arbitrage strategy requires no initial investment, has no risk and yet generates a positive return.)

(4 marks)

(Total for Question: 10 marks)

2.You just bought anewly issued bond which has a face value of $1,000 and pays its coupon once annually. Its coupon rate is 5%, maturity is 20 years and the yield to maturity for the bond is currently 8%.

a.Do you expect the bond price to change in the future when the yield stays at 8%? Why or why not? Explain.(No calculation is necessary.)

(2marks)

b.Calculate what the bond price would be in one year if its yield to maturity stays at 8%.

(2 marks)

c.Find the before-tax holding-period return for a one-year investment period if the bond sellsat a yield to maturity of 7% by the end of the year(year 1).

(2marks)

d.When the ordinary income tax rate is higher than the capital gains tax rate,tax authorities typically tax anticipated price appreciations from bonds at the ordinary income rate in order to prevent tax aversion with discount bonds. Suppose thatfrom the total dollar returnin part c), the coupon payment and the difference between the hypothetical prices in part b) and the purchase price aretaxed at the ordinary income tax rate, 40%. The rest of the dollar return is considered capital gains(due to unanticipated change in yield-to-maturity from 8% to 7%)taxedat30%. In other words, coupon payments and the anticipated price appreciation are taxed at the ordinary income tax rate and the rest at the lower capital gains rate. Using your answers in part b) and c), calculate the after-tax holding period return over oneyear if the yield to maturity is 7% atthe end of the year.

(5marks)

e.Find the realized compound yield before taxes for a two-year holding period, assuming that 1) investorwho bought the newly issued bond now will sellthe bond intwo years, ii) bond's yield-to-maturitywill be7% at the end of the second year, and iii) the coupon in year 1 willbe reinvested for one year at a 3% interest rate. Ignore taxes.

(3 marks)

(Total for Question: 14 marks)

3.Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5)and the last payment in 9 years (at the end of year 9).

a.What is the duration of the pensionobligation? The current interest rate is 10% per yearfor all maturities.

(3marks)

b.To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bondnow? What shouldbe the total face value (not current market value) ofeach zero-coupon bondheld?

(3marks)

c.Right after the fund made its investment outlined in part b), market interest rates for all maturitiesdropped from 10% p.a.to 9% p.a. Show that the investment position constructed in part b) can still fund (approximately) the future payments byshowingthat the fund's net investment is close to 0 at the end of year 9 after making all the scheduled payments.Assume that interest rateswill remain at 9% p.a.Any excess cash from the 5-year investment will be reinvested at 9% and any fractionof the 10-year bonds held can be sold at the going market price at any time to fund the annual payments.

(6marks)

(Total for Question: 12 marks)

4.The current yield curve for default-free zero-coupon bonds is as follows:

Maturity (Years)

YTM

1

10%

2

11%

3

12%

All bonds considered in this question have a face value of $1,000. Assume that the pure expectations hypothesis of the term structure holds.

a.If market expectations are accurate, what arethe expected yieldsto maturity on 1- and 2-year zero coupon bonds next year?

(3 marks)

b.If you purchase a 3-year zero-coupon bond now, what is the expected total rate of return over the next year assumingthat you will sell the bondat the expected price (price that matches the expected yield in part a))?Ignore taxes.

(3 marks)

c.What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?

(3 marks)

d.If you purchase the coupon bond at the price you calculated in part c), what would your total expected rate of return over the next year be (coupon plus price change)? Ignore taxes.

(3 marks)

(Total for Question: 12 marks)

5.

a.Find the Black-Scholes valueofa put option on the followingnon-dividend payingstock:

Time to maturity: 6 months

Standard Deviation: 50% per year

Exercise price: $50

Current stock price: $50

Interest rate: 10%

(4marks)

b.You found that the put option is trading at the fair value you calculated in part a) but the call option with the same exercise price and maturity is currently selling for 9 dollars. Is there an arbitrage opportunity? If so, identify a trading strategy. Explain what actions you would take at the inception and expiry of the strategy to capture an arbitrage profit and calculate the amount of this profit. Show that your strategy eliminates all risk irrespective of the value of the underlying stock at the maturity of the put and call options.

(4marks)

c.You decided to establish a position (unrelated to part a and b) by buying a share of the stock for $50, buying a 6-month put option with exercise price $45, and writing a 6-month call option with exercise price $55. Draw a payoff (not profit and loss) graph to illustrate the outcome of the combined position at expiry. Clearly label all axes and important points, showing relevant numbers on the axes.

(4 marks)

(Total for Question: 12 marks)

6.

a.Consider a one-year futures contract for 1 share of a dividend paying stock. The current stock price is $50 and the risk-free interest rate is 10%p.a. It is also known that the stock will pay a $3 dividend at the end of year 1. The current settlement price for the futures contract is $51. Set up a strategy for an arbitrage profit.What are the initial and terminal cash flows from the strategy? Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk-free rate. There are no margin requirements, transactions costs, or taxes.

(5 marks)

b.Consider a stock that pays no dividends on which a futures contract, a call option and a put option trade. The maturity date for all three contracts is T, the exercise price of the put and the call are both X, and the futures price is F. Show that if X= F, then the call price equals the put price assuming that spot-futures parity and put-call parity conditions hold. Assume that interestis continuously compounded (i.e., use the spot-futures parity with continuously compounded interest).

(5 marks)

(Total for Question: 10 marks)

7.The purpose of this question is to familiarise you with the use of regression analysis to calculate the parameters of the market model and to interpret these parameterestimatesand selected associated statistics. The analysis will enable us to answer questions such as"Did this company outperform or underperform relative to its level of systematic risk?"

Data

You will conduct performance analysis on Apple Inc. with historical monthly data. First, you need Apple's monthly return data. As you did in the first assignment, visit http://finance.yahoo.com. Enter "Apple" or its ticker symbol "AAPL" in the "Get Quotes" box. Then click on "Historical Prices".

Choose "MAX" for time period and "Monthly" frequency, click "Apply", and then "Download Data". Keep only Date and Adj. Close. In the third column, calculate monthly returns in percentage from adjusted prices. Notice that Yahoo Finance matches the first trading day of the month and the closing monthly price (because it also provides monthly opening prices) - for example, what appears to be 1/3/2013adjusted closing price is in fact the endof March 2013price(retrospectively) adjusted for dividend payments.

Calculate monthly returns from January 1981 to August2017- i.e., manually delete the September2017and October2017adjusted prices in Excel after downloading every adjusted close price available from Yahoo Financeand compute monthly returns. Note that you need the December 1980 price to compute the January 1981 return.

You will also need monthly US market excess returns, SMB, HML, and risk-free rates. For those, download the monthly Fama-French factor data from Ken French's website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F_Research_Data_Factors_TXT.zip (no space) and unzip the file. The text file contains monthly and yearly factor data. Delete the descriptions and yearly data and save the text file (in other words, keep only the monthly figures and headings, Mkt-RF, SMB, HML, and RF) and save the text file.

Load the text file in Excel. To do so, click on "Open" in Excel and choose "All Files" at the bottom right corner (as opposed to "All Excel Files" which is the default) to see the text file you saved. Excel will ask what kind of file it is. Choose "Delimited" and click on "Next". Check "Space" as well as "Tab" as delimiters and Excel will load the file correctly - month, Mkt-RF, SMB, HML, and RF in separate columns.

Notice that the return figures in the Fama-French data are in percentage - i.e., 1 means 1 percent or 0.01 - whereas the Apple returns you calculated might be decimal numbers. Align the units of the two series - either decimal numbers or percentage figures.

Merge the two datasets. Double-checkthat the data sets are time-lined correctly after discarding192607 - 198012 observations in the Fama-French dataset.

Calculate Apple's monthly excess returns in another column by subtracting RF from its raw returns. Again, ensure that they are of the same unit - e.g., percentage or raw decimal figures. Now you should have eightcolumnsnow- Month, AAPL Adjusted Price, AAPL Return, Mkt-RF, SMB, HML, RF, and AAPL Excess Return.

Regression

You are required to run the following regression:R_i- R_f=a_i+b_i[R_M- R_f]where R_i, R_f, and R_Maremonthly returns on the stock (AAPL), the riskless security and the market respectively.

You should use the regression function in Excel (Office 2007 version). To access the regression function within Excel you should click on the Data Tab; then locate the "Analysis" group on the menu below (see far right hand side); next click on Data Analysis; then select Regression from the drop down menu - you may have to scroll down to find it and finally click on OK.

Note:If you are using a PC which has notbeen set up to perform regression analysis you will first have to add-in the excel analysis tool pak function. To do this,first click on the Office Button (top left hand corner). At the bottom of the drop down menu click on "Excel Options"; then click on "Add-Ins" in the left hand side pane, then click on "Analysis Tool Pak" in the right hand side pane and on the "Go" button at the bottom. In the pop-up box that appears, click in the small box next to "Analysis Tool Pak". Click on "yes" to install. Finally access the regression function in Excel as described in the above paragraph.

It is recommended that you use Excel Office 2007 version in the University of Auckland student labs. The set-up procedures may differ somewhat for Excel Office 2003.

The regression dialogue box that appears on your screen is shown below(Notice thatyour data ranges would be different).

You should enter the data range for your Y variable (Excess return on Apple) from your Excel spreadsheet into the box described "Input YRange". Similarly, enter the data range for your X variable (Mkt-RF) into the box "Input X Range". This is most easily done by selecting the range for each column in your excel spreadsheet (do not use the range shown in the screenshot).

You may elect to click the "Labels" box. If you click this box your data range for the Y and the X variables MUST include the column headings "R_i-R_f" and "R_M-R_f" or Excel will ignore the first observation in your dataset. If you do not click the Labels box your data range for each column should include numbers only - do not include the column headings in that case. Including the column headings in your data range automatically labels the slope coefficient with its variable name.

Clicking "New Worksheet Ply"places your regression output on a new worksheet.

Next click the small box beside "Line Fit Plots".This automatically generates a line of best fit plot (regression or characteristic line)

Finally, click on "OK"to generate the regression results and line of best fit plot.

To include more than one factors, specify a block of ranges in "Input X Range:" - e.g., $D$4:$F$322" in the example would run a regression with three explanatory variables (factors) located in column D, E, and F.

You are required to:

(i)Gather the data and make necessary adjustments and perform calculations as instructed above. Also print out the first 12observations, monthly figures from September2016to August2017and attach them to your written assignment answersto show that you generated data correctly. (If you are typing your assignment in MS Word, copy and paste the first 12 observations of data from Excel.)

(5 Marks)

(ii)Attach a print out of your Excel results, specifically (1) the Excel regression table (3 rows) showing the coefficients obtained for the intercept and R_M-R_fand (2) the line of best fit plot obtained from your regression output. Based on your Excel output reportand interpret(i.e. provide a brief description of what each of these estimates tells you about AAPL)the following results:

a.a_i , the alpha coefficient.

b.b_i, the beta coefficient

c.R², the coefficient of determination

(10Marks)

(iii)Now estimate Fama-French three factor model by regressing AAPL excess return on MKT-Rf, SMB, and HML and attach the Excel regression table. Comment on Apple's historical performance relative to the expected return from the Fama-French three factor model.

(5Marks)

(iv)Computea) Apple's Sharpe ratio, b) M²measure, and c) Treynor Index based on the data (entire sample period) and interpretthe results. For all standard deviations in this part, use raw returns, not excess returns. For expected excess return (risk premium), use the sample average of excess returns (or average of raw return minus average Rf). Note that in order to obtain raw market returnsyou can addbackR_fto the market excess returnsin the Fama-French dataset.

(10 Marks)

(Total for Question: 30 Marks)