An inherent asset pricing model was used to test the return rate needed for an asset when added to a well-diversified asset. This model measures the asset’s sensitivity to non-diversifying risk (also known as systemic or market risk) but is usually represented by the Beta coefficient and the relationship between the expected return and the theoretical expected return of a risk-free asset. So how to calculate beta of a portfolio? What is the beta of a portfolio comprised of the following securities? Read the following article for more details.
What Is The Beta Of A Portfolio?
The beta or beta is a measure of the systemic risk of a stock or an entire portfolio. Beta shows how well a stock or portfolio’s volatility is relative to the overall market volatility. The beta coefficient of the crypto market is always equal to 1.
You should note the concept of systemic risk. This type of risk affects almost all stocks in the market, many people know that market risks consist of GDP, interest rates, inflation, war … Also, there is a non-systemic risk.
Non-systematic risk A type of risk that affects only stock or a group of stocks. For example, the falling oil price affects the oil and gas group. Still, it is beneficial for the transportation company and vice versa, or the increase or decrease in profit of enterprise A affects firm A’s stock.
For that reason, if the portfolio holds one stock or ten shares with an equal beta coefficient, it will have the same systemic risk level, but a 10-stock portfolio has an unsystematic level of less risk. So diversification reduces non-systemic risk but not systemic risk.
How To Calculate Beta Of A Portfolio?
- Cov (Stock, Market): Cov of the stock’s rate of return and the market’s rate of return.
- Var (Market): variance in the market rate of return.
But rest assured, we don’t need to calculate the beta coefficient for each stock. Most financial websites or stock companies in international markets provide this indicator. However, they often have very different results because they usually take different timelines. However, you can get an approximate result equal to their average, preferably by yourself. (Note: Frequently, financial and securities websites have quite different Beta results).
To summarize: Beta coefficient of the entire portfolio = Beta average of component stocks’ holding rate.
Example: Portfolio X has 2 shares: If stock A (beta = 0.8, weight 40% of assets), stock B (beta = 1.5 weight 60% of assets), then Beta of portfolio X is 0.8 X 40% + 1.5 X 60% = 1.22
Beta cash or bank deposit, we get zero. If you use leverage, multiply the beta multiplier according to the proportion of leverage (This is an easy way, When the beta doubles, then the leverage must be reduced by 4 to optimize profit/risk)
What Is The Significance Of The Beta Coefficient?
Please always keep in mind the meanings of the following metric.
- Beta = 1, the stock is with systemic risk or volatility equivalent to the market (Vn-Index).
- If Beta> 1, the stock has systemic risk or greater volatility than the market (stocks in real estate, finance …)
- Beta <1 indicates a stock with systemic risk or lower volatility than the market (stocks of pharmaceuticals, essential products, and services).
- If Beta = 0, it is independent of market volatility
- Beta <0 moves in the opposite direction with the market
Most stocks have Beta> 0, but sometimes you see beta indicators <0, which means it moves in the opposite direction of the market. However, do not be rigid about sticking to beta; the increase or decrease depends on many other factors.
CAPM Capital Asset Pricing Model And Beta Coefficient
CAPM: A model that evaluates the expected return of an investment in a stock or portfolio relative to systemic risk (beta) and market return.
R = Ro + β X (R tt – Ro)
- R: Reasonable expected return
- Ro: Risk-free rate of return
- β: Beta coefficient of stocks and portfolios
- Rtt: The expected rate of return for the whole market, usually in the long term, is around 10%.
The above formula: You will see why people say the high risk of profit is increased or, relatively, the higher the risk, the higher the profit requirement. We invest in stocks because we take higher risks to expect higher returns.
- Portfolio A has a beta coefficient = 0.5. Portfolio B has a beta coefficient of 2.
- If the yield on a bond, in the US it is Ro = 6%.
- The long term market rate is Rtt = 10%.
- The reasonable expected return of portfolio A will be:
Ra = Ro + beta X (Rtt – Ro) = 6% + 0.5 X (10% – 6%) = 8%
- The reasonable expected return for portfolio B would be:
Rb = Ro + beta X (Rtt – Ro) = 6% + 2 X (10% – 6%) = 14%
If in 2020, the S&P 500 index increases by 48%. Portfolio A with Beta = 0.5 will accept the return: 6% + 0.5 X (48% – 6%) = 27%.
Then portfolio B with Beta = 2 will accept the return: 6% + 2 X (48% -6%) = 93%.
Because the volatility is too large, this is not necessarily the correct way, but depending on the philosophy and method, such as investing in large, medium, or small-capitalization stocks, growth investment, value investment, and careful analysis manage portfolios that require different reasonable returns. If the portfolio has only Beta = 2, the minimum profitability requirement in 2020 must be 60% – 65% or more, then it makes sense. If the portfolio is at 0.5, it only needs to return 27%.
However, it is only a systemic risk. Other risks are non-systemic. Therefore: When you invest with a higher level of risk, the corresponding reasonable required return must be higher. Non-systematic risk can be mitigated by diversifying and distributing money and stocks. But when you invest in high-risk portfolios, be prepared to lose more and more money mentally, but in return, you have the right to demand and expect a greater return.
Above is all the knowledge related to Beta coefficients that you need to know. This article is for informational and educational purposes only. Through this article, we hope you can answer the question, “How to calculate beta of a portfolio?” Finally, wish you all success on your financial investment path. Good luck!