Here is the Question of financial investment, Related to Financial Economics.

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QUESTION:

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.

Hence,

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 + RP0, this is equivalent to

Hence, selecting the portfolio with the highest geometric mean return is optimal for an investor with log utility?


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