To show that the optimal allocation to a single risky asset P is increasing in RP and decreasing in rf , A risk aversion, we can utilize the mean-variance framework developed by Harry Markowitz.
Resolving the problem with the mean variance framework
The mean-variance approach can be used to calculate the best portfolio allocation to a single hazardous asset given a risk-free rate. The utility of the investor, which is influenced by the expected return and variance of the portfolio, is maximized to determine the best allocation. Here are the main conclusions:
- The predicted excess return of the asset over the risk-free rate is what determines the optimal allocation to the hazardous asset. The investor gives the risky asset more weight as the anticipated return rises.
- The ideal distribution is moving away from the risk-free rate. The investor decreases the weight assigned to the hazardous asset as the risk-free rate rises.
- The investor's risk aversion decreases as the optimal allocation increases. A lower allocation to the hazardous asset results from a higher risk aversion.
- As a result of the optimum allocation, the variance of the risky asset is decreasing. A larger variance that implies a higher risk results in a lesser allocation to the hazardous asset.
These correlations show how the optimal allocation to a single hazardous asset in a portfolio is influenced by investor preferences for expected return, risk-free rate, risk aversion, and asset riskiness.