An investment portfolio consists of equal weights in two government bonds of different nations. What correlation level will most likely result in the lowest portfolio standard deviation?A.–0.2B.0.0C.0.5
Question
An investment portfolio consists of equal weights in two government bonds of different nations. What correlation level will most likely result in the lowest portfolio standard deviation?A.–0.2B.0.0C.0.5
Solution
The correlation level that will most likely result in the lowest portfolio standard deviation is -0.2 (Option A).
Here's why:
The standard deviation of a two-asset portfolio is determined by the weights of the assets in the portfolio, the standard deviations of the returns on the assets, and the correlation between the returns on the assets.
The formula for the standard deviation of a two-asset portfolio is:
σp = √[w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * w1 * w2 * σ1 * σ2 * ρ]
where:
- σp is the standard deviation of the portfolio
- w1 and w2 are the weights of the two assets in the portfolio
- σ1 and σ2 are the standard deviations of the returns on the two assets
- ρ is the correlation between the returns on the two assets
In this case, the weights of the two assets in the portfolio are equal, so w1 = w2.
The correlation between the returns on the two assets (ρ) can range from -1 to 1. A correlation of -1 means the returns on the two assets are perfectly negatively correlated (i.e., when the return on one asset goes up, the return on the other asset goes down by an equivalent amount), while a correlation of 1 means the returns on the two assets are perfectly positively correlated (i.e., the returns on the two assets move in the same direction by the same amount).
The lower the correlation between the returns on the two assets, the lower the standard deviation of the portfolio. This is because a lower correlation means the returns on the two assets are less likely to move in the same direction, which reduces the overall volatility of the portfolio.
Therefore, a correlation of -0.2 (Option A) will most likely result in the lowest portfolio standard deviation.
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