According to your personal analysis, the expected return of UBER should be 15.5%. However, this is not necessarily what the CAPM is saying. The expected return on the market is 10.1%, the risk-free rate is 1.8%, and the beta for UBER is 1.12.

You want to exploit the mispricing using an arbitrage portfolio and the recipe from the book. Give the weight in the risk-free asset in percentage.

 

{Give your answer as a percentage with 2 decimals, e.g., if the answer is 0.345224 (or 34.5224%) , enter 34.52 as your answer.}

To determine the weight in the risk-free asset for an arbitrage portfolio, we first need to calculate the expected return of UBER according to the Capital Asset Pricing Model (CAPM).

The CAPM formula is given by:

\[
E(R_{\text{UBER}}) = R_f + \beta \cdot (E(R_{\text{market}}) - R_f)
\]

Where:
- \(E(R_{\text{UBER}})\) is the expected return according to CAPM.
- \(R_f\) is the risk-free rate.
- \(\beta\) is the beta of UBER.
- \(E(R_{\text{market}})\) is the expected return of the market.

### Step 1: Plug in the known values

\[
E(R_{\text{UBER}}) = 1.8\% + 1.12 \cdot (10.1\% - 1.8\%)
\]

\[
E(R_{\text{UBER}}) = 1.8\% + 1.12 \cdot 8.3\%
\]

\[
E(R_{\text{UBER}}) = 1.8\% + 9.296\%
\]

\[
E(R_{\text{UBER}}) = 11.096\%
\]

### Step 2: Compare the expected return from CAPM with the actual expected return

The actual expected return for UBER is given as 15.5%, which is higher than the CAPM-based return of 11.096%.

### Step 3: Arbitrage portfolio weights

Now, we want to exploit this mispricing using an arbitrage portfolio. The arbitrage strategy involves taking a position where we can profit from the mispricing by shorting or buying the asset and adjusting the weight in the risk-free asset.

The weight \( w_{\text{risk-free}} \) in the risk-free asset is calculated as:

\[
w_{\text{risk-free}} = \frac{E(R_{\text{UBER}})_{\text{actual}} - E(R_{\text{UBER}})_{\text{CAPM}}}{E(R_{\text{market}}) - R_f}
\]

Substitute the known values:

\[
w_{\text{risk-free}} = \frac{15.5\% - 11.096\%}{10.1\% - 1.8\%}
\]

\[
w_{\text{risk-free}} = \frac{4.404\%}{8.3\%}
\]

\[
w_{\text{risk-free}} \approx 0.530
\]

### Step 4: Convert to percentage

\[
w_{\text{risk-free}} \approx 53.01\%
\]

Thus, the weight in the risk-free asset is **53.01%**.

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How does arbitrage work in the context of the CAPM model?
2. What are the risks associated with arbitrage strategies?
3. How does beta influence the expected return in the CAPM formula?
4. What assumptions does CAPM make about market conditions?
5. Can CAPM be applied to other asset pricing models, such as multifactor models?

**Tip:** Arbitrage strategies often require quick adjustments to remain effective as market prices converge.

According to your personal analysis, the expected return of UBER should be 15.5%. However, this is not necessarily what the CAPM is saying. The expected return on the market is 10.1%, the risk-free rate is 1.8%, and the beta for UBER is 1.12. You want to exploit the mispricing using an arbitrage portfolio and the recipe from the book. Give the weight in the risk-free asset in percentage.

Learn how to calculate the weight in the risk-free asset for UBER using the CAPM formula. The problem explores key financial concepts such as the expected return, risk-free rate, and arbitrage. The solution uses CAPM and arbitrage strategies to determine the weight in percentage for an arbitrage portfolio. Suitable for undergraduate finance students.

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