Question

In this exercise, we will implement a simplified version of the "Betting Against Beta" (BaB) strategy. For this purpose, we construct a zero-cost market-neutral (zero-beta) strategy by taking a levered position in portfolio 1 (the lowest-beta portfolio) and a delivered short position in portfolio 5 (the highest-beta portfolio) using the portfolio betas each year. a) Compute the returns of a levered version of portfolio 1 that has the same beta as the market portfolio. What is the average annual return of this portfolio? Assume that the riskless rate can be used for both borrowing and lending.

b) How does your conclusion in d) of Question 2 change in terms of the feasibility of exploiting mispricing in a CAPM world?

Answer 1

a) To compute the returns of a levered version of portfolio 1 that has the same beta as the market portfolio, we need to adjust the returns of portfolio 1 to match the beta of the market portfolio. Let's assume the beta of the market portfolio is βm, and the beta of portfolio 1 is β1.

The formula to compute the levered returns is as follows:

Levered Returns = βm * (Market Returns - Risk-Free Rate) + Risk-Free Rate

In this case, since we want the levered version of portfolio 1 to have the same beta as the market portfolio, we can set βm = β1.

Assuming we have the market returns data and the risk-free rate for each year, we can calculate the levered returns for each year using the formula above. Then, we can compute the average annual return by taking the average of these levered returns.

b) In terms of the feasibility of exploiting mispricing in a CAPM world, the conclusion in d) of Question 2 would likely change. In a CAPM world, mispricing opportunities are assumed to be quickly eliminated by rational investors who adjust their portfolios based on the expected returns and risk levels predicted by the CAPM model.

If the CAPM model holds and is widely accepted, mispricing opportunities would be limited, and it would be challenging to consistently exploit these opportunities for abnormal profits. Rational investors would quickly adjust their portfolios based on the expected returns and risk levels implied by the CAPM, leading to the elimination of mispricings.

However, it's important to note that the real-world financial markets are complex and may not fully adhere to the assumptions of the CAPM model. Market inefficiencies, behavioral biases, and other factors can create opportunities for mispricing to occur. Therefore, it is essential to consider additional factors and conduct further analysis to assess the feasibility of exploiting mispricing in any given market environment.

Step-by-step explanation:

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Answer 2

a) Compute the levered portfolio returns using the formula \(R_{\text{levered}} = R_{\text{risk-free}} + \beta_{\text{market}} \times (R_{\text{market}} - R_{\text{risk-free}})\).

b) Evaluate the feasibility of exploiting mispricing in a CAPM world considering market efficiency and expected returns.

a) To compute the returns of a levered version of portfolio 1 with the same beta as the market portfolio, you can use the following formula:

\[ R_{\text{levered}} = R_{\text{risk-free}} + \beta_{\text{market}} \times (R_{\text{market}} - R_{\text{risk-free}}) \]

where:

- \( R_{\text{levered}} \) is the return of the levered portfolio.

- \( R_{\text{risk-free}} \) is the risk-free rate.

- \( \beta_{\text{market}} \) is the beta of the market portfolio.

- \( R_{\text{market}} \) is the return of the market portfolio.

b) Without the details provided in Question 2, it's challenging to directly address the conclusion in d). However, in a CAPM world, the feasibility of exploiting mispricing is often influenced by assumptions about market efficiency and the accuracy of expected returns. If market mispricing is pervasive and persistent, it might present opportunities for profit. Conversely, if markets are highly efficient and prices quickly reflect all available information, exploiting mispricing becomes more challenging. Assessing the feasibility of exploiting mispricing in a CAPM world requires considering factors like transaction costs, information asymmetry, and the speed of market adjustments.