Risk Based Measures of Performance App ...
Finance academics and professionals have developed several returns-based measures to assess the value... Read More
Strategic asset allocation involves deciding among the various securities within a portfolio and the relative weightings of each. Asset allocation differs from Investor to Investor as the optimal mix depends on the investor’s preferences. The utility theory helps formalize these human preferences into a mathematical equation. According to utility theory, the optimal asset allocation is the one that is expected to provide the highest utility to the investor, given the investor’s investment time horizon.
The most straightforward asset allocation decision would be to mix risky and risk-free assets. The formula below allows for the calculation of the weight of the risky asset in the portfolio:
$$ w^\ast=\frac {1}{\lambda} \left[\frac { (\mu-r_f) }{ \sigma^2 } \right] $$
Where:
Asset allocations are the result of a process of analysis and study. Portfolio managers can use various methods, which can frequently change with technology. However, at the highest level, managers must decide on a trusted process and go through the necessary iterations to determine the asset allocation that best enhances the client’s wealth.
Question
According to the optimal choice equation, increasing the variance of the returns on the risky asset most likely affects the weight of the risky asset in the portfolio?
- Reduce weight.
- Not enough information.
- Increase weight.
Solution
The correct answer is A:
Mathematically, the formula shows the returns’ variance in the fraction’s denominator. Increasing this denominator will decrease the quotient, and the resulting weight afforded to the risky asset.
Theoretically, this also makes sense because more significant variances mean the asset is subject to more powerful swings and significant unknowns. Leaving all other factors of the decision equal, the risky asset should be afforded less weight in the portfolio since it is more volatile, a method of taming the volatility by increasing the presence of the risk-free asset. This will keep the original outcome the same.
B is incorrect. The optimal choice equation provides enough information to determine the effect of increasing the variance of the returns on the risky asset. The equation shows how the optimal weight of the risky asset depends on the expected return, the risk-free rate, the risk aversion coefficient, and the variance of the risky asset. Therefore, if we know these parameters, we can calculate the optimal weight of the risky asset for any given level of variance.
C is incorrect. It contradicts the optimal choice equation. The equation implies that the optimal weight of the risky asset is inversely proportional to the variance of the returns on the risky asset. Therefore, if the variance increases, the optimal weight decreases, and vice versa. Intuitively, this means that the investor will increase the exposure to the risky asset as its riskiness decreases, and allocate less wealth to the risk-free asset.
Reading 4: Overview of Asset Allocation
Los 4 (g) Recommend and justify an asset allocation based on an investor’s objectives and constraints