I’m gonna talk about the risk and return of portfolio. An investment portfolio is any collection or combination of financial assets. Portfolio Risk and Return
When you bought 3 company shares, these company shares are your portfolio.
If we assume all investors are rational, and therefore risk averse,
then investors will always choose to invest in portfolios, rather than in single assets.
Investors will hold portfolios, because it will diversify away a portion of the risk that is
inherent in “putting all your eggs in one basket”. Remember, don’t put all your eggs in one basket. If an investor holds a single asset,
he or she will fully suffer the consequences of poor performance.
The goal is to form a well-diversified portfolio of assets. So that the risk will become lower.
Portfolio Return
To calculate the portfolio return,
we take the weighted average of the returns on the individual assets from which it is formed.
Based on this formula, portfolio return can be calculated by taking
the summation of the weight of each asset, times the return of the asset.
Portfolio Standard Deviation
To calculate the portfolio standard deviation, this is the formula we apply.
Example: Portfolio Weights
Let’s take an example.
Suppose you have $15,000 to invest, and you have purchased securities in the following amounts. What are your portfolio weights in each security? To get the weight of Security A, you just need to take $2,000 over $15,000, then you will get 0.133. Do the same for B, C, and D, then you will get 0.2, 0.267, and 0.4.
Consider the portfolio weights computed previously, if the individual stocks have
the following expected returns, what is the expected return for the portfolio?
By taking the weights multiply with the returns, you will get the portfolio return, 15.41%.
Example: Portfolio Return and Risk
Let’s try the next question. Consider the following information, where you invest
50% in Asset A, another 50% in Asset B, and the returns for each state of economy are estimated. Boom means good time, whilst bust means bad time.
Calculate the return and standard deviation for each asset, then for the portfolio. First, get the expected return and standard deviation for each asset. For Asset A, by taking 0.4 times 30% + 0.6 times negative 10%, you will get 6%.
Then, take 30% minus 6%, square it, times 0.4, plus negative 10% minus 6%,
square it, times 0.6, you will get the variance for Asset A, 384.
Then, open square root for the variance, you will get the standard deviation for Asset A, 19.6%.
For Asset B, follow the same way. Then you’ll get return 13%, and standard deviation 14.7%.
Next, get the expected return and standard deviation for the portfolio. The first step is to calculate the portfolio return in boom. Taking 0.5 times 30% plus 0.5 times negative 5%, you will get 12.5%.
Then calculate the portfolio return in bust. Taking 0.5 times negative 10% plus 0.5 times 25%, you will get 7.5%.
Expected portfolio return can be calculated by
taking 0.4 times 12.5% plus 0.6 times 7.5%, you will get 9.5%.
Before you can calculate the standard deviation, you need to get the variance first. By taking 0.4 times 12.5% minus 9.5%, square it, plus 0.6 times 7.5% minus 9.5%,
also square it, then you will get the variance of portfolio. Open square root of the variance, you will get the standard deviation of portfolio = 2.45%.
One thing that you may take note, portfolio return lies between return of Asset A and Asset B.
But, the portfolio risk is very much lower than the risk of Asset A and Asset B.
That’s the reason of forming a portfolio. Do remember that, portfolio can diversify the risk, which means, it can reduce the risk. Another method of calculating the portfolio risk is by using this formula.
First, you need to calculate the covariance. After this, the next step is to calculate the variance of portfolio. Then you can get the standard deviation, as shown here.
Risk of a Portfolio
Combining two investments can reduce the portfolio risk. However, it has to happen under certain conditions. Diversification is enhanced,
depending upon the extent to which the returns on assets “move” together.
This movement is typically measured by a statistic known as correlation,
as shown in the figure below.
If two investments are moving together, going up and down together, they are positively correlated. But if one going up while the other one going down, they are negatively correlated. Only when two investments are negatively correlated will reduce the overall risk. Generally, investing in more than one security can reduce risk. But if two stocks are perfectly positively correlated,
diversification has no effect on risk, which means the risk cannot be reduced.
However, if two stocks are perfectly negatively correlated, the portfolio is
perfectly diversified, which means t
