π Investment and risk
When it comes to investments, "risk" does not necessarily mean loss, it means it is uncertain whether it will rise or fall.
We cannot predict the future, but if we can measure the risk size of our portfolio of various stocks, we will be able to respond calmly to risks.
So let's see how to measure risk in an investment.
π Variance and standard deviation of return π-The smaller the result, the smaller the variation
The variance is calculated by squaring the deviation of the expected "expected return (return on investment)" in the actual market and the "expected return" according to the economic phase, and multiplying by each economic probability again.
Standard deviation is the value of the variance being rooted and reduced.
In other words, it is a value of how far my expected return is from the expected rate of return, so the larger the standard deviation, the greater the fluctuation, which can be said to be a dangerous stock.
After finding the standard deviation and substituting it into π in the following equation, the probability of fluctuation from the expected rate of return to the following range can be calculated.
±1π: 68.27%
±2π: 95.45%
±3π: 99.73%
π Coefficient of Variation-The smaller the result value, the smaller the risk of taking against the desired rate of return.
Let's say you have two assets, one with low risk and return and the other with high risk and return.
At this point, the coefficient of variation is the tool by which you can determine which asset is more reasonable to invest in.
Coefficient of change = π (standard deviation of asset return) / average (expected) rate of return of the asset
For example, let's say you have the following two funds:
| fund | average return on the fund | Standard deviation |
| A | 8% | 10% |
| B | 10% | 12% |
The coefficients of change for Funds A and B are 1.25 and 1.2, respectively.
This means that the risks I have to take to get the expected return of 1 unit I want are 1.25 and 1.2, respectively, so the smaller the coefficient of variation the better.
π Covariance and correlation coefficient between the two asset returns-The smaller the result, the greater the diversification effect.
If there are stocks with similar fluctuation trends in my portfolio, it can be said that there is not much value as a diversification investment.
As a typical example, in a situation where the travel industry is difficult due to the epidemic, it is better to drive investments as a single company because any airline shows a similar trend.
"Covariance" and "correlation coefficient" are the indicators that tell whether two different assets are moving similarly or in different directions.
If the value of the covariance is positive, it indicates that the stock moves in the same direction, and if the value of the covariance is negative, it is located above and below the average return.
However, since the range of values ββfor covariance is not limited, in practice, a uniform correlation coefficient in the range of -1 to 1 is used for accurate comparison.
And, rather than comparing two assets, we usually find the correlation coefficient between market returns and individual assets.
If the correlation coefficient is +1, it does not exist in reality because it is a stock that moves exactly the same as the market.
And if the correlation coefficient is 0, the asset has nothing to do with the flow of the market.
Therefore, when investing, we can properly see the effect of diversification if we construct a portfolio of assets with different correlation coefficients.
π Systematic and unsystematic risks
What we have seen above so far has been a method of reducing investment risk through diversification. The risk that can be reduced through diversification is called “unstructured risk”.
However, after a certain level, there is a market risk that is no longer reduced by diversification alone. This is called "systematic risk".
Systematic risk exists because it cannot exist in the world of stocks that can move completely in the opposite direction and offset risk with zero.
You can't reduce this, but you can prepare for it by measuring the risk rate through the "beta factor".
π Beta coefficient-The higher the beta value, the greater the risk (the greater the rise or fall).
The beta coefficient is an indicator of the sensitivity of individual stocks to the stock market.
For example, if π½ = 1.2, when the market fluctuates by 1, the stock changes by 1.2, so it is classified as a risky stock.
This is because if the beta is greater than 1, the loss is the same as the yield is greater.
In addition, if the stock price of the stock rose by 2% when the overall stock market rose by 1% one day, 1.2% is classified as an increase due to systematic risk and 0.8% as an increase due to unsystematic risk.
If the beta for each stock is greater than 1, it is called an aggressive stock (high beta), and it is less than 1 and is called a defensive stock (low beta).
The beta (rate of change in market conditions) of the entire portfolio, not individual stocks, is calculated as a weighted average according to the investment weight as follows.
| Holding stock | Share of investment in holdings (a) | Beta coefficient (b) | a X b |
| A | 30% | 0.8 | 0.24 |
| B | 20% | 1.0 | 0.2 |
| C | 50% | 1.2 | 0.6 |
| Sum | 100% | 1.04 |
We can take the beta of the individual stock or the beta of the portfolio to calculate the "return demand" I want.
Required rate of return = real free risk interest rate + inflation compensation rate + risk compensation rate
The beta coefficient affects the “risk compensation rate” in the above equation.
The risk compensation rate, also known as the risk premium, is the part that requires investors to receive more than the nominal risk-free rate (real risk-free rate + inflation compensation rate) because they take risks.
Risk compensation rate = beta coefficient X risk premium in the stock market (expected rate of return in the stock market-the nominal no-risk interest rate in the stock market)