Judge the Risk by Portfolio

When the investors put their money into the stock market, it means that they must take the risk of the stock market, because risk is one of the natural qualities of the stock market. One company easy to get a poor performance and its stocks will go down. Therefore, there will be no way to complete avoid risk, but judge it. In finance, risk is best judged in a portfolio context. Because the possibility that many companies gets serious performances, and their stock price go down at the same time is lower than for only one company. This essay will discuss that why the portfolio context is the best way to judge the risk in the finance market. The first part will introduce the basic theories for portfolios. The methods of measuring risks and value of the portfolio will be explained in the second part to demonstrate that why it is better select portfolios. The third part will give the example of family groupings on performance of portfolio selection in the Hong Kong stock market. The conclusion will be given at the end of the essay.

Firstly, the theory of portfolio and the five suppositions of portfolio selection need to be explained before the following discussion of the value of portfolios. The article ‘Portfolio Selection’, which was issued on Journal of Finance in 1952 and the book ‘Portfolio Selection: Efficient Diversification of Investments’ which was published in 1959 was known as the opening if the modern portfolio theory. The author of these two literatures is Harry M. Markowitz who was born in 1927, in America, and was awarded the Nobel Prize for Economics in 1990 for his outstanding contribution in economics. Simply speaking, the portfolio theory is that containing various securities and other assets in one collection of the investor, and of this collection could reach the highest return in the given level of risk or the minimum risk for the given level of return, and then this group could be called Efficient Portfolio. Portfolio not only have the characteristic of return and risk for the single stock, also have the peculiarity of returns and risks of the relationships which between those stocks.

Besides the meaning of portfolio theory, the five suppositions are required to be mentioned. They are the premise of portfolio theory. The first supposition is that investors assess the stocks and portfolios just depend on the expected returns and risks. The second hypothesis is that investors are rational. There are two aspects of this hypothesis. The first is that investors are unsatisfied. They always want to see more returns if other conditions are the same. Therefore, if there are two portfolios with the same standard deviation, investors will choose the one which has higher returns. The other aspect of this supposition is that investors are tired of risk. The big difference between the actual return and the average of returns will be not wanted by the inventors. They prefer to the stable portfolios. It means that inventors will choose the portfolio which is less risky than others in the same expected returns. The third supposition is that investors hold the assets for a period. Then the fourth supposition is about the measurement for assessing the information. This means that, for the same information of a given portfolio, all investors will do the same expected return and the level of risk. The last supposition is that the market is frictionless. Under this supposition, the transaction cost, such as the tax, handing charges, will be slight. All the stocks can be divided innumerable, and the information is available. The portfolio theory is developed on these five suppositions by Markowitz (1952).

Whether the portfolio could reduce the risk does not be proved by speaking, but through evidences which be calculated with the special measurement, value at Risk (VAR), a methodology for measuring portfolio risk. Under this method, the largest loss that will be suffered by the portfolio through all truly exceptional periods can be estimated. Moreover, the potential loss on a portfolio of assets can be assessed by VAR. One portfolio may include many different assets, like bounds, stock. However, now the portfolio will just include two stocks to get the ideas clear and easy to understand. First, the volatilities of the returns of each stock need to be estimated, because the volatilities of the portfolio relates to the volatility of the returns of both stocks in the portfolio. However, stock returns will not always constant; they may co-vary, as well. In some conditions, the covariance of two stocks may be negative, and the result is that if one of their returns goes up, then the return of the other will goes down. As each stock has its own volatility and they will hardly to be the same to each other, the effect of putting two different stocks together is that the swing in return will be inhibited. This is the reason why the volatility of a portfolio is lower than the volatility of each single stock in the portfolio, and more stocks in the portfolio, more reduction of the volatility. The value of the covariance between the stock’s returns is required. It will be used together with the volatility to calculate the volatility of the portfolio, and then the VAR of the portfolio will be found.
In order to explain how to calculate, suppose A has invested $1 in stock 1, 2, and 3, then the daily volatility of the portfolio would be:

Volatility (portfolio) = Volatility (stock 1) + Volatility (stock 2) + Volatility (stock 3)
+ 2×covariance (stock 1, stock 2)
+ 2×covariance (stock 1, stock 3)
+ 2×covariance (stock 2, stock 3)

As the formula shows, if covariance (stock 1, stock 2), covariance (stock 1, stock 3), and covariance (stock 2, stock 3) were zero, the volatility of the portfolio is the result of collecting each stock’s volatility together. Therefore, the VAR of the portfolio is the sum of each stock’s VAR. However, the covariance is not always zero, and the VAR of the portfolio could not be calculated by simply plus the VAR of each stock together. The co-variances between assets are needed to be estimated, and the constant volatility or time-varying method can be used to calculate the VAR. (Hopper, 1996)

One of the examples for employing the portfolio theory in practice is within-family portfolio in Hong Kong. There are many companies belonged to a family and these companies are controlled by one business conglomerate. The local journalistic and newspaper are keeping a watchful eye on the ownership of this family. For example, ‘ some stocks are referred to as falling into the Li Ka Shing stable, or the Y. K. Pao stable etc.’ (Lam, 1994) Mok et al (1989) is the first person who discovered the ‘price of constituent stocks controlled by a family tend to move together more than the price of stocks controlled by different family.’ And this opinion comes from the factor analysis of 48 stocks. From the study of Mok et al (1992), a case was discovered that the mean residual return correlation (0.161) of within-family is more than 3 times (3.3 times) higher than the average number (0.049) of residual return correlation of between-family-group. In particular, family manage stocks in a new way to organize homogeneous stock grouping, it could lead to a good selection of portfolio. This sentence was investigated in the study of Kin Lam, Herry M. K., Iris Cheung, and H.C. Yam in 1994. They used the Full Historical model, the Overall Mean model, the Single-Index model, and the Multi-Index model which are conventional approaches in the forecasting of future correlation matrix and the establishment of portfolios to promote the usefulness of the family group. In one family group, they can choose a sizeable portfolio together and this group is affected by the relationships between the members of a family. They can range a bigger portfolio than one individual investor and easy to control and manage the risks based on the trust between each other. Several decision makers work in the trust will provide the investors more confidence to survey the risk from multiply aspects and easier to make a right final resolution. (Middleton, 2008)

To sum up, portfolio theory is affecting the current investment strongly, most of investors and companies manage their risky assets using portfolio context. There are not only one form to assess the risk and benefit of the portfolio. Since this theory was worked out by Markowitz in 1956, the steps of chasing the greatest return has never stopped. From Markowitz’s Mean-Variance model to the Multi-Index model, more and more evidence can offer the benefit of the portfolio selection. Different types of investment were developed, and more efficient measurements were discovered to develop the theory more advanced. In total, it is no doubt that the portfolio context is the best choice to judge the risk so far.

Reference:

Hopper, G. P., (1996), Value at Risk: A New Methodology for Measuring Portfolio Risk, Business Review.
Lam, K., Henry M.K., Mok et al, Cheung, I., and Yam, H.C., (1994), Family Groupings on Performance of Portfolio Selection in the Hong Kong Stock Market, Journal of Banking and Finance.
Markowitz, H. M., (1952), Portfolio Selection, Journal of Finance.
Middleton, C. A. J., (2008), An Investigation of the Benefits of Portfolio Investment in Central and Eastern European Stock Markets, Research in International Business and Finance.