# What is the weight of risky asset in the optimal complete portfolio?

I have 5 different stocks in a market value weighted portfolio. I found that the expected return of this portfolio is 0,008444379 and the variance is 0,001498836. I know that the risk free rate is 0,4%. My risk aversion is 4 and I assume the 1 risky asset, 1 risk-free asset world. If the risky asset is the market value weighted portfolio of the five stocks, how can I find what is its weight in the optimal complete portfolio?

• But the expected return of my risky portfolio is 0,844% and the risk-free rate is 0,4%.
– pao
Commented Jan 25, 2022 at 8:11
• Okay I read that as 0.0084%. I see what you mean now. Commented Jan 25, 2022 at 20:49
• "My risk aversion is 4" out of what? Commented Feb 24, 2022 at 20:15

Theory says that the "Market Capitalized Weighted" portfolio is the Max Sharpe Ratio Portfolio. Short term data suggests otherwise.

how can I find what is its weight in the optimal complete portfolio?

Find the Sharpe Ratio of different weightings (expected return - risk free rate / sqrt(variance)) by using Excel Solver to allocate all possible weights to the 5 risky asset, or using programming e.g. Python.

The one with max Sharpe Ratio is the optimal portfolio in general. To adjust for risk tolerance, deleverage that optimal portfolio using Cash, or leverage that optimal portfolio using Margin. You do not achieve a lower variance simply by choosing a worse sharpe ratio.

On the "risk aversion is 4", it involves plotting the "Utility and Indifference Curves" over the Graph of the Max Sharpe Ratio Line (with deleveraging and leveraging).

• Thank you for your explanation. Can I find the weight also using the formula (expected return-risk-free rate)/A*variance ?
– pao
Commented Jan 25, 2022 at 8:35
• You can find the correct weight by testing all possible values of Asset 1,2,3,4,5, starting from 100%,0%,0%,0%,0%. Commented Jan 25, 2022 at 8:54