The returns on X and Y are perfectly negatively correlated. The standard deviation on these securities are 25 and 15 per cent respectively. How much needs to be invested in X to eliminate risk?

To eliminate risk, we need to find the amount of investment in X that will offset the returns from Y. Since the returns on X and Y are perfectly negatively correlated, any investment in X will completely offset the risk from Y.

To calculate the amount needed to invest in X, we need to consider the standard deviations of X and Y. The standard deviation measures the volatility or risk of an investment.

Let's assume we want to invest an amount "x" in X. The risk from X can be calculated as x * standard deviation of X, which is 25x.

To eliminate the risk, the amount invested in X should be equal to the risk from Y, which is given by the formula: risk from Y = investment in X * standard deviation of Y.

Substituting the values, we have: 15% = 25x * 15%

Simplifying the equation, we get: 0.15 = 0.25x * 0.15

Dividing both sides by 0.25 * 0.15, we find: x = 0.15 / (0.25 * 0.15)

Solving the equation, we get: x = 0.15 / 0.0375 = 4

Therefore, to eliminate risk, we need to invest 4 times the amount in X compared to Y.