Provide graphs of the security market line and the actual position of the five portfolios for both time periods.

Words: 1106
Pages: 5
Subject: Finance

FINANCIAL ECONOMICS

Instructions

 The coursework counts towards 20% of your assessment. Check Sussex Direct for the submission deadline. The coursework is individual work, carried out upholding the values of academic integrity.




Note that the official limit of 1500 words is not a target. In fact, please make sure your answers are clear and concise. You will most likely need far less than 1500 words for your solution.
 You can find the marking scheme for this problem set on page 4.

Q1. CAPM test [65 pts]

This question asks you to test CAPM by looking at the historical performance of stocks using Excel. The data are in CAPM data 2022.xlsx on Canvas. We will focus on five risky assets: four stock portfolios called small-low, small-high, big-low, big-high, and a value-weighted stock index that we will treat as the market portfolio. Here “small” and “big” refer to market capitalization, while “low” refers to growth stocks (low book-to-market ratios), and “high” refers to value stocks (high book-to-market ratios). Thus for example the small-low portfolio is a portfolio of growth stocks with small market capitalization. The data set runs from January 1927 to December 2021 and contains excess (simple) returns Ri −Rf (where Rf is the return on 90-day Treasury bills) for all five risky portfolios.
1
Here is a recommended set of steps that will allow you to answer assessed questions (a)-(d) below. Note: in step 1–5 we will focus on the period 1/1927-12/1963 only. In step 6, we repeat the same analysis for the period 1/1964-12/2021. Your solution for Q1 should consist of answers to questions (a)-(d) below.

1. Download the data from Canvas and calculate the (arithmetic) average excess returns for the five risky portfolios during the period 1/1927-12/1963.

2. Calculate the betas of the five portfolios during 1/1927-12/1963. Use the SLOPE func- tion in Excel that computes the slope coefficient βi of a linear regression
Ri −Rf = αi + βi (Rm −Rf) + εi
Note that you have been provided the excess market returns.

3. Calculate the alphas of the five portfolios during 1/1927-12/1963 using the INTERCEPT function in Excel. (The intercept is, by definition, the alpha.)

4. Calculate the expected excess returns predicted by CAPM for this period. According to the CAPM equation we should have E[Ri]−Rf = βi (E[Rm]−Rf). Compute this for all five portfolios, including the market portfolio. (You can take the average excess return of the market portfolio from step 1 as your estimate of the expected excess market return.)

5. Plot the security market line predicted by CAPM, as well as the actual position of the five portfolios in (beta, expected excess return) space.

6. Now repeat the steps above for the time period 1/1964-12/2021.

Your solution for Q1 should include the following:

(a) Provide tables reporting the mean excess return, beta, alpha, and the CAPM predicted excess return for the five portfolios. Round the numbers to three decimal places. For each of the two time periods you should have a completed table as below: [25 pts]

Table 1: CAPM test Small Big Low High Low High Market mean excess return beta alpha CAPM pred. excess return
2

(b) Provide graphs of the security market line and the actual position of the five portfolios for both time periods. [25 pts]

(c) Provide a brief comment on the difference between the CAPM predicted mean excess returns and the actual mean excess returns in the two periods. You can also do this comparison by looking at the magnitude of the alphas (which represent the difference between the predicted and actual mean excess returns). Compare the two time periods: does CAPM hold in either period? [5 pts]

(d) Which portfolio has the highest alpha? Provide a brief comment. [10 pts]

Q2. Portfolio choice [35 pts]

Suppose you are a fund manager, managing an active fund with an expected return of 16% and a standard deviation of 25%. There is also an index fund tracking the FTSE 100, which has an expected return of 12% and a standard deviation of 20%. The risk-free rate is 4%.

(a) Calculate the Sharpe ratio of your active fund and the index fund. Compare the ratios and provide an interpretation in no more than four sentences. [10 pts]

Your client has 75% of their wealth invested in your fund and the remaining 25% in the risk-free asset.

They consider switching their risky investment to the index fund.

(b) Calculate the expected return and the risk (standard deviation) of a portfolio with 75% invested in the index fund and 25% in the risk-free asset. [5 pts]

(c) Suppose your client does not want to exceed the risk level found in part (b). Calculate the maximum expected return that they can achieve under this condition by combining your fund with the risk-free asset. What portfolio allocation (i.e., what combination of the risk-free asset and one of the risky funds) should your client choose? [10 pts]

(d) What is the fee (as a percentage of the investment in your fund) you could charge your client to make them indifferent between investing in your fund or the index fund? [10 pts]

3

Marking scheme Your solutions will be marked based on the following criteria. For more information on the School’s generic marking criteria, see the Assessment Information page on Canvas.
Specific marking criteria for problem set Points Generic criteria

Q1
Are the required numbers in the tables correct? 20
Knowledge & Under- standing; Application

Is the presentation of the tables clear? Are the numbers rounded to three decimal places?
5 Presentation & Style
Are the graphs correct? Do they include all required elements (the SML and the actual po- sition of the five portfolios)?
20

Knowledge & Under- standing; Application

Is the presentation of the graphs clear? Are the axes and the required elements clearly labelled?
5 Presentation & Style

Are the comments on the performance of CAPM and the magnitude of the alphas cor- rect? Are the comments clearly and concisely communicated?
15

Knowledge & Under- standing; Critical Think- ing; Presentation & Style

Q2

Does the solution clearly lay out the key steps? Are the key steps and the final answers cor- rect? Are the interpretations clearly and con- cisely communicated?
35

Knowledge & Under- standing; Application; Critical Thinking; Pre- sentation & Style
4