Question

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· How do you compute the expected return and risk of a portfolio?

Answer 1

The expected return on an investment is the expected value of the probability distribution of possible returns it can provide to investors. The return on the investment is an unknown variable that has different values associated with different probabilities. Expected return is calculated by multiplying potential outcomes (returns) by the chances of each outcome occurring, and then calculating the sum of those results

In the short term, the return on an investment can be considered a random variable that can take any values within a given range, with some distinct probabilities. The expected return is based on historical data, which may or may not provide reliable forecasting of future returns. Hence, the outcome is not guaranteed. Expected return is simply a measure of probabilities intended to show the likelihood that a given investment will, on average, generate a positive return, and what the likely return will be.

The purpose of calculating the expected return on an investment is to provide an investor with an idea of the probable return on an investment that carries some level of risk, such as a stock or mutual fund. This gives the investor a basis for comparison with the risk-free rate of return, as well as with the eventual actual return that the investor receives. The interest rate on 3-month U.S. Treasury bills is often used to represent the risk-free rate of return.

Expected Return

The expected value of the distribution of returns from an investment

The expected return on an investment is the expected value of the probability distribution of possible returns it can provide to investors. The return on the investment is an unknown variable that has different values associated with different probabilities. Expected return is calculated by multiplying potential outcomes (returns) by the chances of each outcome occurring, and then calculating the sum of those results

In the short term, the return on an investment can be considered a random variable that can take any values within a given range, with some distinct probabilities. The expected return is based on historical data, which may or may not provide reliable forecasting of future returns. Hence, the outcome is not guaranteed. Expected return is simply a measure of probabilities intended to show the likelihood that a given investment will, on average, generate a positive return, and what the likely return will be.

The purpose of calculating the expected return on an investment is to provide an investor with an idea of the probable return on an investment that carries some level of risk, such as a stock or mutual fund. This gives the investor a basis for comparison with the risk-free rate of return, as well as with the eventual actual return that the investor receives. The interest rate on 3-month U.S. Treasury bills is often used to represent the risk-free rate of return.

Basics of Probability Distribution

Calculating Expected Return of a Portfolio

Calculating expected return is not limited to calculations for a single investment. Expected return can also be calculated for a portfolio. The expected return for an investment portfolio is the weighted average of the expected return of each of its components.(weighted by the percentage of the portfolio’s total value that each component of the portfolio accounts for). Examining the weighted average of various portfolio assets can also help investors assess the diversification of their investment portfolio.

To illustrate the expected return for an investment portfolio, let’s assume the portfolio is comprised of investments in three assets – X, Y, and Z – and that $2,000 is invested in X, $5,000 invested in Y, and $3,000 is invested in Z. Assume that the expected returns for X, Y, and Z have been calculated and found to be 15%, 10%, and 20%, respectively. Based on the respective investments of $2,000, $5,000, and $3,000 in each component asset, then the portfolio’s expected return can be calculated as follows:

Expected Return of Portfolio = 0.2(15%) + 0.5(10%) + 0.3(20%)

= 3% + 5% + 6%

= 14%

Thus, the expected return of the portfolio is 14%.

Note that although the simple average of the expected return of the portfolio’s components is 15% (the average of 10%, 15%, and 20%), the portfolio’s expected return of 14% is slightly below that simple average figure, due to the fact that half of the investor’s capital is invested in the asset with the lowest (10%) expected return rate.