the objective of asset allocation is to find an investment portfolio so that the investors degree of happiness is greatest.

Certainty Equivalent := The certainty equivalent represents the amount of guaranteed money an investor would accept now instead of taking a risk of getting more money at a future date.

Risk-Premium:=

• A risk premium is the investment return an asset is expected to yield in excess of the risk-free rate of return.
• Investors expect to be compensated for the risk they undertake when making an investment. This comes in the form of a risk premium.

Markowitz Allocation:

1. INPUT: Markowitz assumes the investor has precise estimates for:

   1. $\mu$ (column vector of returns for all investable assets)

   2. $\Sigma$ (covariance matrix of all investable assets)

   3. $\sigma_{n,m}$ (the n/m entry of Sigma)

   4. $\rho_{n,m}$ (the correlation of n/m assets return)

   5. $\sigma_p^2$ (variance of a portfolio p)

   6. $r_f$ (risk-free rate)

   7. $U$ (investors utility function/measurement of happiness)

   8. $\gamma$ (investor´s degree of risk aversion)

   9. $W$ (investor´s wealth)

2. ACTIVE DECISION MAKING:

3. $w_p$ (column-vector of portfolio weights)

4. $\mu_p$ (expected return of portfolio w_p)

5. $\sigma_p^2$ (return variance of portfolio w_p)

6. CHARACTERIZING RETURN DENSITY OF OPTIMAL PORTFOLIO

7. $w_f$ (column-vector for the portfolio on the Efficient Frontier)

8. $\mu_f$ (scalar, stands for the expected return of an efficient Portfolio)

9. $\sigma_f^2$ (scalar, return variance of efficient Portfolio)

10. $w_{TP}$ (column-vector with the weights of the Tangency Portfolio)