Expected return and standard deviation graph

Investment And Security Market

Group Project FIN 320 – Fall 2020 Part I Total Points: 37.5 This part of the project deals with portfolio return/risk calculations. To complete the project, you will hand in a set of answers to the questions listed below along with any supporting calculations and graphs. This project should be neat and well organized so that I can easily find your answers to each of the questions. 1. Data: This project makes use of annual data for two risky securities: the S&P 500 Index and Gold.

Annual values for each of these securities during the 29-year period from 1975-2003 are provided in a spreadsheet named GroupProject1Data.xls. The spreadsheet is available on the class web page. You will also need an estimate of the annual risk-free rate. To get this rate, you should take the most recent annual rate on U.S. Government Securities (note: select the Treasury Security you feel is most relevant for a one-year investment horizon). These rates can be found on the following web page: http://www.federalreserve.gov/releases/H15/update/

List your estimate of the annual Risk-Free rate here: ______________________ What date did you use to identify this interest rate? ______________________ What U.S. Treasury category did you use to identify this rate? ______________________

2. Return Calculations: Calculate annual returns for each of the two securities for each of the 28 years from 1976 through 2003. Calculate the average annual return, the standard deviation of annual returns, and the correlation between the returns of the two securities during this period and fill in the table provided. (Note: all of these calculations are based on annual security returns not index values). Attach the spreadsheet showing all of the relevant calculations as Exhibit 1.

S&P 500 Gold

Average Annual Return Standard Deviation of Annual Returns Return Correlation(S&P,Gold)

http://www.federalreserve.gov/releases/H15/update/
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3. Capital Allocation Lines: Assume that the mean return, standard deviation, and correlation estimates you calculated above provide a reasonable forecast of the expected returns and risks of these securities for the coming year. Based on these forecasts, plot the two risky securities on an expected return – standard deviation graph. Also, plot the risk-free security. Be sure to label all three securities on the graph. Draw the Capital Allocation Line for each of the risky securities (S&P and Gold). Attach the graph as Exhibit 2.

4. Risky Portfolios: Calculate the expected returns and standard deviations of portfolios that combine the

two risky securities (S&P and Gold), varying weights from 0% to 100% in increments of 5% (note: this should result in 21 portfolios). Attach the spreadsheet showing all relevant calculations as Exhibit 3.

5. The Opportunity Set and the Optimal Risky Portfolio: Plot the risk-free security and the 21 portfolios

described in question 4 on an expected return – standard deviation graph. Be sure to clearly label the S&P 500, Gold, and the risk-free security on the graph. Identify and label the Minimum Variance Portfolio on the graph. Identify and label the Optimal Risky Portfolio on the graph and draw the Capital Allocation Line (CAL) for this portfolio. Attach the graph as Exhibit 4. What are the portfolio weights in the Optimal Risky Portfolio? ____________________________

What is the standard deviation of the Minimum Variance Portfolio? ____________________________ 6. Capital Allocation using the Optimal Risky Portfolio: Pick a target annual return between 2% and 10%.

Using the risk-free security you identified above and the Optimal Risky Portfolio you found in question 5, calculate the portfolio weights (in the risky and risk-free) that would be required to achieve this target annual return. Calculate the standard deviation of this portfolio. Label this point on the graph in Exhibit 4 and fill in the table below.

Optimal Risky Portfolio

Target Annual Return Weight in the Optimal Risky Portfolio

Weight in the risk-free security

Portfolio standard deviation

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7. Sensitivity Analysis: (a) Repeat questions 4 and 5 assuming the correlation between the two risky securities is ρ=0.30 (but

using the same expected return and standard deviation forecasts). Attach the spreadsheet showing all relevant calculations as Exhibit 5 and the expected return – standard deviation graph as Exhibit 6.

What are the portfolio weights in the Optimal Risky Portfolio? ______________________

What is the standard deviation of the Minimum Variance Portfolio? ______________________

How do the Minimum Variance Portfolio, the Optimal Risky Portfolio, and the CAL for the Optimal Risky Portfolio compare to those from question 5?

(b) Repeat question 6 assuming using the Optimal Risky Portfolio from question 7(a). Fill in the table

below. (Note: Use the same target return as in question 6.)

Optimal Risky Portfolio

Target Annual Return Weight in the Optimal Risky Portfolio

Weight in the risk-free security

Portfolio standard deviation

How does the standard deviation of this portfolio compare to that from question 6? (c) What do the results from questions 7(a) and 7(b) tell us about the relation between security

correlations and diversification?

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Group Project FIN 320 – Fall 2020 Part II Total Points: 37.5

The second part of the project deals with the Capital Asset Pricing Model and Market Model estimation of the CAPM. To complete the project, you will hand in a set of answers to the questions listed below along with any supporting calculations and graphs. 1. Data: This project makes use of weekly returns for one year on a market index (the S&P 500) and two

international Exchange Traded Funds (ETFs) listed on the American Stock Exchange. You will use the S&P 500 as a proxy for the “market portfolio”. You will then choose two international ETFs from among the international funds listed on the American Stock Exchange web page (go to http://www.amex.com/etf/prodInf/EtPiMain.jsp and select “international” to see a list of these ETFs). Weekly prices for each of the ETFs with sufficient data are provided in a spreadsheet named GroupProject2Data.xls. The spreadsheet is available on the class web page. You can use the data from the spreadsheet or obtain the data from the AMEX web site. Throughout the project, you will assume an annual risk-free rate of 1.5%. You can estimate the weekly risk-free rate by dividing the annual rate by 52.

2. Return Calculations: Calculate weekly returns for the S&P500 and each of the international funds for each of the 52 weeks during the sample period (note: there are 53 weekly prices to calculate 52 weekly returns). For each security, calculate the mean return, standard deviation, and variance of weekly returns, and fill in the relevant data in the table below. Be sure to list the ticker symbols for the international funds you have chosen. (Note: these summary calculations are based on weekly returns not prices). Attach the spreadsheet showing all relevant calculations as Exhibit 1.

Summary Statistics for Weekly Returns Mean Return Standard Deviation Variance

S&P 500 International Security 1: Ticker = International Security 2: Ticker = Risk-free rate - -

3. The Capital Market Line: Using the mean returns and standard deviations you calculated in question 2, plot the S&P 500 (the market) and the two international funds on an expected return – standard deviation graph. Using the weekly risk-free rate given above, draw the capital market line (CML). Be sure to label all of the securities (including the risk-free security) on the graph. Attach the graph and related calculations as Exhibit 2. Are the positions of the international securities on the graph consistent with CAPM? Why or why not?

http://www.amex.com/etf/prodInf/EtPiMain.jsp
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4. The Market Model: Calculate weekly excess returns for each of the international funds and the S&P 500 (the market) by subtracting the weekly risk-free rate from each weekly return. For each of the two international funds, create an X-Y scatterplot with the excess returns of the international fund on the Y- axis and the excess returns of the market (S&P) on the X-axis. Add a trendline (security characteristic line) to each graph. Using either the trendline options or other excel functions, calculate the Alpha and Beta for each of the international funds and fill in the related information in the table below. Attach the graph and related calculations as Exhibit 3.

Market Model Estimates Alpha Beta R2

S&P 500 International Security 1: Ticker = International Security 2: Ticker =

5. Market vs. Firm-Specific Risks: One of the benefits of the market model is that it allows us to decompose

total risk (variance) into two components. Using the equation we discussed in class, calculate the market component of risk and the firm-specific component of risk for each of the securities. Fill in the related table below and Attach any related calculations as Exhibit 4.

Decomposition of Risk Total Risk Market Risk Firm-Specific

Risk S&P 500 International Security 1: Ticker = International Security 2: Ticker =

Which of the three securities is the riskiest based on total risk? How does your answer change if you consider only systematic risk? How does your answer change if you consider only firm-specific risk?

6. The Security Market Line: Using the risk-free rate and the mean returns and Betas of the international

securities and the market (S&P), create an expected return – beta graph. Be sure to label all of the securities on the graph (including the risk-free security). Draw the Security Market Line (SML) for this set of securities. Attach the graph and related calculations as Exhibit 5. Are the international funds priced correctly according to CAPM? If not, what would be your buy/sell recommendations for these international funds?