Assignment 3 Portfolio Theory, CAPM, And Efficient Markets ✓ Solved

Assignment3portfolio Theory Capm And Efficient Markets

Assignment #3: Portfolio Theory, CAPM, and Efficient Markets 1. There are two stocks in the market, stock A and stock B. The price of stock A today is $75. The price of stock A next year will be $63 if the economy is in a recession, $83 if the economy is normal, and $96 if the economy is expanding. The probabilities of recession, normal times, and expansion are 0.2, 0.6, and 0.2, respectively.

Stock A pays no dividends and has a correlation of 0.8 with the market portfolio. Stock B has an expected return of 13 percent, a standard deviation of 34 percent, a correlation with the market portfolio of 0.25, and a correlation with stock A of 0.48. The market portfolio has a standard deviation of 18 percent. Assume the CAPM holds.

a. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why?

b. What are the expected return and standard deviation of a portfolio consisting of 70 percent of stock A and 30 percent of stock B?

c. What is the beta of the portfolio in part (b)?

2. A portfolio that combines the risk-free asset and the market portfolio has an expected return of 9 percent and a standard deviation of 13 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 12 percent. Assume the CAPM holds. What expected rate of return would a security earn if it had a 0.45 correlation with the market portfolio and a standard deviation of 40 percent?

3. Suppose the market is semi-strong form efficient.

Can you expect to earn excess returns if you make trades based on:

  • a. Your broker’s information about record earnings for a stock? Explain.
  • b. Rumors about a merger of a firm? Explain.
  • c. Yesterday’s announcement of a successful new product test? Explain.

4. A company has changed how it accounts for inventory. Taxes are unaffected, although the resulting earnings report released this quarter is 20% higher than what it would have been under the old accounting system. There is no other surprise in the earnings report, and the change in the accounting treatment was publicly announced earlier. Assume market efficiency. Will the stock price be higher when the firm releases the earnings report? Explain.

5. Which of the following statements are true about the efficient market hypothesis? Please explain your reasoning for each statement.

  • a. It implies perfect forecasting ability.
  • b. It implies that prices reflect some set of information.
  • c. It implies an irrational market.
  • d. It implies that prices do not fluctuate.
  • e. It results from keen competition among investors.

Sample Paper For Above instruction

The assessment of asset pricing models, particularly the Capital Asset Pricing Model (CAPM), and their implication in efficient markets are central topics in financial economics. This paper explores these issues through the analysis of two stocks, the application of CAPM for expected returns, and the examination of market efficiency, especially in the context of semi-strong form efficiency.

Preference Between Stock A and Stock B for Risk-Averse Investors

The decision between Stock A and Stock B hinges on their expected returns, risks, and correlation with the market. Stock A's future potential depends on economic states, with prices varying significantly: $63 in recession, $83 in normal, and $96 in expansion, with associated probabilities. Calculating the expected return of Stock A involves multiplying each possible outcome by its probability and summing these: E(R_A) = (0.2 (63 - 75)/75) + (0.6 (83 - 75)/75) + (0.2 * (96 - 75)/75). This yields an expected return that captures the weighted average of potential gains or losses relative to its current price.

Stock B offers a straightforward expected return of 13% with known risk characteristics and a low correlation with the market, at 0.25. Given risk aversion, investors prefer less risky assets that provide favorable risk-return trade-offs aligned with the CAPM. Since Stock B has a lower standard deviation (34%) than the market and a moderate return, its beta (which measures systematic risk) can be derived from its correlation with the market and its standard deviation. The beta of Stock B is calculated as beta_B = correlation_B * (standard deviation_B / market_std). For Stock A, since it has a high correlation (0.8) with the market but unknown standard deviation, the focus is on its risk-adjusted expected return relative to systematic risk. The investor would prefer Stock B if the expected return considering its risk aligns more favorably with their utility function, especially considering diversification benefits.

Expected Return and Standard Deviation of a Portfolio

The portfolio's expected return is the weighted average of component assets: E(R_P) = 0.7 E(R_A) + 0.3 E(R_B). The standard deviation requires considering the variances and covariances since the assets are not perfectly correlated. The portfolio's variance formula is: var_Rp = (w_A)^2 var_A + (w_B)^2 var_B + 2 w_A w_B cov(A,B). The covariance between A and B can be calculated using their standard deviations and correlation: cov(A,B) = correlation_AB SD_A * SD_B. Once the covariance is obtained, the standard deviation is the square root of the variance, which reflects the overall risk of the portfolio.

Portfolio Beta Calculation

The beta of the portfolio is a weighted sum of individual asset betas: beta_P = w_A beta_A + w_B beta_B. Here, beta_A can be derived from the correlation between stock A and the market, or directly through the formula beta_A = correlation_A * (SD_A / market_SD). The data suggest a high correlation with the market for stock A and a lower correlation for stock B, indicating differing systematic risks. Portfolio beta indicates the sensitivity of the portfolio to market movements, critical for assessing expected returns using CAPM.

Return Prediction for a Security and Market Efficiency

Using the CAPM, the expected return of a security with a correlation of 0.45 and a standard deviation of 40% is calculated as E(R) = Rf + beta (E(R_m) - Rf), where beta can be approximated from the correlation and standard deviations: beta = correlation (SD_security / SD_market). The market's alpha is zero under CAPM, so expected returns are solely explained by systematic risk. The high correlation relative to the market's risk level indicates a potentially higher expected return based on CAPM assumptions.

Regarding market efficiency, the semi-strong form asserts that all publicly available information is already incorporated into stock prices. Therefore, making trades based solely on publicly available information such as earnings records, rumors, or recent announcements should not yield abnormal profits beyond normal market risks. Consequently, stock prices adjust rapidly to such information, rendering attempts to earn excess returns futile. For example, a trader cannot consistently profit from record earnings announcements or rumors about mergers because the market quickly prices in this information.

Impact of Changes in Accounting and Market Efficiency Hypotheses

Changes in accounting methods that do not affect fundamental economic value but alter reported earnings can temporarily influence stock prices due to investors' reactions or perceptions. If the market is efficient, the stock price should reflect all available information, including the accounting change. Since the earnings report is higher but publicly announced and no other surprises exist, the stock price is expected to adjust accordingly, reflecting the updated earnings figure.

The efficient market hypothesis (EMH) suggests that stock prices incorporate all relevant information. The statements under review are critically analyzed: EMH does not imply perfect forecasting, but prices reflect available information; it supports the idea that markets are efficient due to the keen competition among investors; however, it does not imply prices do not fluctuate, rather they fluctuate based on new information.

In conclusion, understanding how stocks are valued under the assumptions of CAPM and market efficiency provides insight into rational investment strategies and the limits of outperforming the market through publicly available information. Investors should recognize the probabilistic nature of expected returns and the importance of diversification and risk management within an efficient market paradigm.

References

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  • Barberis, N., Shleifer, A., & Wurgler, J. (2005). Comovement. Journal of Financial Economics, 75(2), 283-317.
  • Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance, 48(1), 65-91.
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