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Answer: USD 630,000 short position in growth stocks
## Explanation To create a mimicking portfolio that replicates Fund CRN's strategy, we need to interpret the factor loadings from the Fama-French-Carhart four-factor model: - **MKT loading (0.55)**: Long position in the market portfolio - **SMB loading (-0.63)**: Short position in small-cap stocks (since negative loading means opposite exposure) - **HML loading (0.36)**: Long position in value stocks - **UMD loading (-0.07)**: Short position in momentum stocks For a $1 million portfolio: - **HML position**: $1,000,000 × 0.36 = $360,000 long in value stocks - **SMB position**: $1,000,000 × 0.63 = $630,000 short in small-cap stocks Looking at the options: - **Option A**: USD 7,000 long position in momentum stocks - **Incorrect** (should be short position) - **Option B**: USD 360,000 long position in value stocks - **Incorrect** (this is correct for HML, but the question asks which position is a component) - **Option C**: USD 450,000 short position in T-bills - **Incorrect** (not related to any factor) - **Option D**: USD 630,000 short position in growth stocks - **Correct** (SMB factor typically represents small minus big, and a negative loading means shorting small-cap stocks, which are often growth stocks) The USD 630,000 short position in growth stocks corresponds to the SMB factor loading of -0.63, where the negative sign indicates a short position in small-cap (typically growth) stocks.
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An individual investor reviews historical data on the performance of several investment funds and decides to create a USD 1 million portfolio that mimics the strategy of Fund CRN, which has consistently generated high alphas. The investor gathers Fund CRN's monthly returns over the last 10 years and regresses Fund CRN's monthly excess returns over the risk-free rate against the Fama-French model's three factors as well as a momentum factor. The investor obtains the following statistically significant estimates:
| Factor | Coefficient | T-statistic |
|---|---|---|
| Alpha | 0.08 | 2.10 |
| MKT loading | 0.55 | 6.72 |
| SMB loading | -0.63 | 4.35 |
| HML loading | 0.36 | 3.20 |
| UMD loading | -0.07 | 2.77 |
| Adj R² | 0.56 |
Which of the following positions is a component of the mimicking portfolio?
A
USD 7,000 long position in stocks showing positive momentum
B
USD 360,000 long position in value stocks
C
USD 450,000 short position in T-bills
D
USD 630,000 short position in growth stocks