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:

MeanStandard DeviationCorrelation

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+0.5Br\_{1} = 0.5A + 0.5B

Suppose the benchmark has the following returns:

r_2=0.4A+0.6Br\_{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)P(r\_{1} > r\_{2})

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