Calculating Risk and Return of a Two Asset Portfolio

Summary

This video explains how to calculate the expected return and risk of a portfolio, focusing on the key concepts of expected return, portfolio variance, and standard deviation. Using a two-asset example, the expected return of a portfolio is calculated by multiplying the return of each asset by its weight and summing the results. The risk of the portfolio is measured through variance, incorporating asset weights, standard deviations, and covariance. The video provides formulas and a clear walkthrough of calculations, making it a valuable guide for understanding portfolio management.

Takeaways

• 😀 The expected return of a portfolio is calculated by summing the expected return of each asset multiplied by its weight.
• 😀 The formula for expected return involves multiplying the expected return of each asset by its weight in the portfolio and adding the results.
• 😀 For a portfolio with two assets, the expected return of asset A is 10%, and asset B is 5%.
• 😀 Asset A has a weight of 60%, while asset B has a weight of 40% in the example portfolio.
• 😀 To calculate the expected return of the portfolio, multiply the expected returns by their respective weights and sum the results, which gives an 8% expected return in this case.
• 😀 Portfolio risk is typically measured using portfolio variance or standard deviation, denoted by sigma p.
• 😀 Portfolio variance is the square of the standard deviation of the portfolio.
• 😀 In the given example, asset A has a standard deviation of 10% and asset B has a standard deviation of 5%.
• 😀 The portfolio variance calculation also involves the covariance between assets A and B, which is 0.5 in this case.
• 😀 The portfolio variance formula includes terms for the squared weights and standard deviations of assets A and B, and twice the product of their covariance and weights.

Q & A

What is the formula for calculating the expected return of a portfolio?

The formula for calculating the expected return of a portfolio is the summation of each asset's expected return multiplied by the weight of that asset in the portfolio. This is done for all assets in the portfolio.

What are the expected returns and weights of assets A and B in the example given?

In the example, asset A has an expected return of 10% and makes up 60% of the portfolio. Asset B has an expected return of 5% and makes up 40% of the portfolio.

How do you calculate the expected return of the portfolio in the example?

To calculate the expected return of the portfolio, multiply the expected return of asset A (10%) by its weight (60%) and the expected return of asset B (5%) by its weight (40%). Adding these values gives the total expected return of 8%.

What is portfolio risk typically measured by?

Portfolio risk is typically measured by the portfolio's variance or standard deviation.

What does variance represent in the context of portfolio risk?

Variance represents the square of the standard deviation, which measures the spread of asset returns around the expected return, indicating the level of risk in the portfolio.

What are the standard deviations and weights of assets A and B in the portfolio example?

In the example, asset A has a standard deviation of 10% and a weight of 60%, while asset B has a standard deviation of 5% and a weight of 40%.

What is covariance in the context of portfolio risk, and what is its value in the example?

Covariance measures how two assets move together. In the example, the covariance between assets A and B is 0.5.

What formula is used to calculate the portfolio variance in the example?

The formula to calculate the portfolio variance is: (weight of asset A squared * standard deviation of A squared) + (weight of asset B squared * standard deviation of B squared) + 2 * (covariance of A and B * weight of A * weight of B).

How do you calculate the portfolio variance in the example?

To calculate the portfolio variance: (0.6^2 * 0.1^2) + (0.4^2 * 0.05^2) + 2 * (0.5 * 0.6 * 0.4) gives a total portfolio variance of 0.2.

What is the total portfolio variance in the example?

The total portfolio variance in the example is 0.2.