- 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 One Portfolio Outperforming Another Portfolio

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 reach a target return of $5 million. Let us look at the following three options and find out the probability of reaching our target in each case:

- Entire $10 million in Asset A
- Entire $10 million in Asset B
- $5 million in A and $5 million in B

Assuming r as the return from each portfolio, our objective can be expressed as follows:

P (10million*r > 5million)

Or

P (r > 0.5)

We know that if the returns of an asset are normally distributed, it can be expressed as a function of standard normal distribution. We can associate the return distribution to a standard normal distribution, which has a zero mean and a standard deviation of one.

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