Suppose you manage a small fund of $100 million fully invested in small stocks. Assume the riskfree rate is zero. Assume further that you find only 60 such stocks worthy of investing.

If the second stock has a weight of w2 = −0.02, how much money will you put into it? (in millions)

Question

Suppose you manage a small fund of $100 million fully invested in small stocks. Assume the riskfree rate is zero. Assume further that you find only 60 such stocks worthy of investing.

If the second stock has a weight of w2 = −0.02, how much money will you put into it? (in millions)

BlackTom AI · Accepted Answer

We start from the given information: the fund size is 100 million, the second stock has a weight w2 = -0.02 (negative indicating a short position), and there is no risk-free component affecting the calculation.
To determine how much money to allocate to stock 2, multiply the total capital by the stock's weight: amount = w2 × total capital = (-0.02) × 100 million = -2 million.
The negative sign signifies a short position, i.e., borrowing shares to sell now with the expectation of buying them back later at a lower price.
Now evaluate each option:
- -20 million (short): This would correspond to a weight of -0.20 (since -20 million / 100 million = -0.20). That does not match the given weight of -0.02, so this is incorrect.
- 2 million (long): This corresponds to a weight of +0.02, not -0.02, so it contradicts the specified negative weight and is incorrect.
- 20 million (long): This would be a weight of +0.20, again not matching the given -0.02 and also implying a long rather than short position, so incorrect.
- -2 million (short): This exactly matches the weight -0.02 on a 100 million fund, reflecting a short position of 2 million of capital.
Thus, the correct interpretation is a short position of 2 million in stock 2, while the other options either misstate the magnitude or the direction (long vs short) based on the provided weight.

Suppose you manage a small fund of $100 million fully invested in small stocks. Assume the riskfree rate is zero. Assume further that you find only 60 such stocks worthy of investing. If the second stock has a weight of w2 = −0.02, how much money will you put into it? (in millions)单项选择题

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