Lessons

- Mean, Variance, Standard Deviation and Correlation
- Constructing an Efficient Frontier
- Minimum Variance Hedge Ratio
- What is Serial Correlation (Autocorrelation)?
- Diversification and Portfolio Risk
- Value at Risk (VaR) of a Portfolio
- Probability of One Portfolio Outperforming Another Portfolio
- Probability of Attaining a Return Goal

# Probability of Attaining a Return Goal

Earlier we looked at calculating the probability of beating a fixed target. Now we will look at calculating the probability of beating a benchmark which is itself stochastic.

Let us consider two assets A and B with the following details:

Mean | Standard Deviation | Correlation | |

A | $\mu\_{A}=10%$ | $\sigma\_{A}=20%$ | $\rho\_{AB}=30%$ |

B | $\mu\_{B}=12%$ | $\sigma\_{B}=26%$ |

We have a total of $10 million to invest. Our objective is to beat a benchmark.

Let us take the 50-50 portfolio, which has the following returns:

$r\_{1} = 0.5A + 0.5B$

Suppose the benchmark has the following returns:

$r\_{2} = 0.4A + 0.6B$

We need to find that probability that our portfolio will beat the benchmark index, i.e., $P(r\_{1} > r\_{2})$

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