Here is the Question of financial investment, Related to Financial Economics. You need to give an accurate answer:
VaR – Telser’s Criterion:
Recall that the α% Value-at-Risk (VaR) RL is given by the return such that α% of returns are below RL.
P(Rp < RL) ≤ α
Assuming again that returns are normally distributed, we obtain for the constraint
E[RP] ≥ RL – Φ–1 (α)σP
Where Φ–1 is the inverse of the standard normal cdf and, thus, gives the VaR at level α.
One could now choose the portfolio with the highest E[RP] that satisfies this constraint (Telser’s criterion).
One problem is that the choice set might be empty.
Figure: Optimal Portfolio Choice – Telser’s Criterion
Log-Utility and Geometric Mean Returns:
Suppose investors with wealth ω0 maximize the following utility function
max E[lnω1] – lnω0
Since ω1 = (1 + RP)ω0, this is equivalent to
Hence, selecting the portfolio with the highest geometric mean return is optimal for an investor with log utility?