Beta and Standard Deviation as Measurement of Risk - Example

Beta and Standard Deviation as Measurement of Risk Name: Tutor: Course: Date: Introduction The expected return and beta coefficient are two important measures used to evaluate respectively the profitability and risk of investing in different investment portfolios. The expected return measures and estimates the expected rate of the return of a given investment portfolio, while, beta coefficient measures the volatility of a given investment portfolio with that of the market as a whole. Usually, investment portfolios available in the market have varying returns, since some portfolios have higher returns compared to others (Ilmanen, 2011). However, the element of volatility is also an essential consideration for investment decision making processes. This is because some stocks have higher returns as well as higher volatility in comparison to investment portfolios based on the historical volatility of the investment portfolios. Furthermore, some investment portfolios are more volatile compared to the market volatility. Therefore, the expected returns and beta value are considered appropriate measures of evaluating investment profitability and risk. In the analysis of investment portfolios, in addition to beta, the standard deviation can be used to measure and assess the volatility of a given stock. The standard deviation is related to the annual rate of return and is derived by determining the dispersion of the historical returns from the expected annual rate of return of a given stock. Therefore, investors can use the standard deviation to measure the volatility of the expected returns of investment portfolios. In general, investment portfolios which are more volatile have higher standard deviation compared to those with lower standard deviation. Therefore, the higher volatility of the returns of an investment portfolio indicates that the investment portfolio is a riskier investment compared to that which is less volatile (McNeil, Frey & Embrechts, 2005). The beta coefficient on the other hand, measures the volatility of an investment portfolio compared to that of the market. Therefore, the beta value is used to assess whether the volatility of a stock is more or less than the market volatility. The beta coefficient is derived using regression analysis by regressing the returns of an investment portfolio on the market returns. Subsequently, if the beta value is equal to 1, it implies that the volatility of the investment portfolio is same with that of the market. Therefore, the returns of such an investment portfolio will move with that of the market. On the other hand, if the beta value is less than 1, it implies that the investment portfolio is less volatile compared to the market volatility. However, if the beta value of an investment portfolio is greater than 1, it implies that the volatility of the investment portfolio is higher than that of the market (Tofallis, 2008). Therefore, the expected return and the beta value are of great significance in risk-return evaluation. This is because the expected return estimates the returns from a given investment, while the beta value indicates the volatility for the different investment portfolios in the market. Therefore, the two measures provide the investors with appropriate insight on the returns and risk level of investing in the various available investment portfolios, thus enabling the investors to make informed decisions (Shim & Siegel, 2008). In general, investment portfolios with higher expected returns tend to be more volatile and thus have a higher risk associated with them compared to the investment portfolios with lower expected returns. Similarly, the beta value indicates the level of volatility and risk associated with a given investment portfolio. This implies that there is a relationship between the level of risk and returns of investment portfolios. Objectives The objectives of this case study include; To establish the relationship between the level of risk and the expected return of an investment portfolio. To determine whether investment portfolios with higher risk have higher expected return. To establish whether there are increasing returns to risk. Literature Review In econometric models, beta is a very significant measure used in the evaluation of market securities. This is because it indicates the price responsiveness of a given investment portfolio to the demand and supply forces in the securities market. Typically, the ‘offensive’ stocks usually have higher values of beta, which are usually greater than one. However, the less aggressive ‘defensive’ stocks have relatively lower values of beta, which are usually less than one (Brailsford, Reaney & Bilson, 2004). A widely used approach in the estimation of the beta value is the market model approach, whereby the return of the security is regressed against the market return. Previous studies show that the relationship between beta and return exists but is dependent of other factors. According to Haugen (2012), there exist a positive relationship between volatility and returns only in very brief time periods. The study of relationship between risk and returns on investments has recently been of great interest to researchers and practitioners in the financial markets. This is mainly because of the profitability associated with the industry. Therefore, several researches continue to focus on the relationship between the two measures which are the expected returns and beta. In general, the literature overview relating to beta-return relationship illustrates several areas of interest in the financial markets. These include risk assessment and profitability analysis of different investment portfolios available in the market (Ilmanen, 2011). However, within the broad diverse literature of risk and profitability analysis, the focus primarily lies on two major areas. These two primary areas of focus in the investment analysis include the beta and expected returns of the investment portfolios in the market. Indeed, the recognition of consumer satisfaction generating consumer lifetime value is evident. The level of risk and expected returns are closely related to investment decisions. The current study explores the risk-return relationship to determine and evaluate how the two measures relate and how they influence investors in their decision making. Several researches have established that investment decision is significantly determined by the returns expected to be derived from a given investment portfolio. According to Tofallis (2008), investment decisions are usually based on the expected returns from an investment portfolio. Therefore, the establishment and evaluation of the factors that influence rate of return is of great importance in the financial markets. Consequently, this area continues to be of great interest to researchers. This is majorly because the study of the bet-return relationship provides further understanding of trends associated with different investment portfolios traded in the financial markets. Data analysis The sample data comprised of five listed stocks in the Hong Kong market. The five stocks include ordinary shares of AcrossAsia, Timeless Software, Transport International Holdings, Tysan Holdings and Universe International Holdings. The variables collected for the respective stocks included their price index from 1st January, 2001 to 1st December, 2013. The summary statistics of the Hong Kong market return and the returns of the respective five stocks over the given period is as illustrated in table 1 below. As indicated in table 1, the average monthly market return in the Hong Kong market from 1st January 2001 to 1st December, 2013 is (M = 0.41%, SD = 6.39). The median of the market monthly returns is 1.28, which seems to differ significantly with the mean. The difference between the maximum monthly market return (21.34%) and the minimum monthly market return (-21.99%) in the Hong Kong market is 43.33%. Table 1: Summary statistics   Market returns Returns of AASI Returns of TIME Returns of TRANS. INTL Returns of TYSAN Returns of UNIV Mean 0.41 -2.24 -1.25 -0.04 1.64 -0.24 Standard Error 0.5130 2.1160 1.6509 0.5304 1.1216 1.7969 Median 1.28 0.00 -3.77 0.46 0.00 -1.01 Mode #N/A 0 0 0 0 0 Standard Deviation 6.3874 26.3445 20.5534 6.6032 13.9637 22.3712 Sample Variance 40.7990 694.0312 422.4433 43.6027 194.9848 500.4725 Kurtosis 1.6511 5.9534 1.4556 2.2309 4.0697 1.9051 Skewness -0.5444 -0.8547 0.2316 -0.4744 0.2391 0.4424 Range 43.33 218.12 127.71 46.80 109.47 142.54 Minimum -21.99 -138.63 -65.81 -27.24 -54.00 -63.84 Maximum 21.34 79.49 61.90 19.56 55.47 78.70 Sum 63.13 -346.70 -194.04 -5.74 253.82 -36.45 Count 155 155 155 155 155 155 Figure 1 below illustrates the histogram of monthly returns of AcrossAsia shares in the Hong Kong stock exchange market. Figure 1 As illustrated by the histogram in figure 1, the distribution of the monthly returns of AcrossAsia is approximately symmetrical. This indicates that the distribution of monthly returns of AcrossAsia is similar to that of the normal distribution. Figure 2 Figure 2 above illustrates the histogram of the Timeless Software monthly returns included in the sample. As illustrated by the histogram, the distribution of the sample data for the monthly returns of Timeless Software shares in the Hong Kong stock exchange market is also approximately symmetrical. This also indicates that the distribution of Timeless Software monthly returns is bell-shaped and approximately normal. Figure 3 Figure 4 Figure 5 The histogram of Tysan Holdings and Universe International Holdings monthly returns are indicated in figure 4 and 5 respectively. The two histograms are also approximately symmetrical. However, the histogram of Transport International Holdings monthly returns is slightly left-skewed. This suggests that the monthly returns of the Transport International Holdings price index have a skewed distribution. Therefore, based on the histograms illustrated above the distribution of the monthly returns of AcrossAsia, Timeless Software, Tysan Holdings and Universe International Holdings are approximately normal. According to the empirical rule, for a normal distribution, 68% of the values fall within one standard deviation from the average return, 95% within two standard deviations from the average return and 99.7% of values fall within 3 standard deviations from the average return. Empirical results The regression summary results of the simple regression models used to determine the beta values by regressing the monthly returns of the individual stocks on the monthly Hong Kong monthly returns are indicated table 2 below; Assuming single model index the estimated beta values of the selected five companies are as indicated in the table below; As indicated in table 2, AcrossAsia has the highest beta value of approximately 1.3393, while Transport International Holdings has the lowest beta value of approximately 0.5022. Therefore, of the five companies selected, the beta values of AcrossAsia and Universe International Holdings are higher that of the market (Beta = 1), while the beta values of Timeless Software, Transport International Holdings and Tysan Holdings are lower than that of the market. Table 2: Beta Values Company Beta 1. ACROSSASIA 1.3393 2. TIMELESS SOFTWARE 0.8368 3. TRANSPORT INTL. HLD. 0.5022 4. TYSAN HOLDINGS 0.9366 5. UNIVERSE INTL. HLD. 1.2298 Table 3 below indicates the average return of the respective five companies. The average return relates to the period from 1st January, 2001 to 1st December, 2013. Within this period the average market monthly return in the Hong Kong stock exchange market is approximately 0.41%. As indicated in the table, the mean monthly return of Tysan Holdings is highest among the selected five companies. Furthermore, among the selected five companies listed in the Hong Kong stock exchange market, Tysan Holdings is the only company with a positive mean monthly return of 1.64% over the period starting 1st January, 2001 and ending 1st December, 2013. Table 3: Beta and Average Returns Company Beta Average Return 1. ACROSSASIA 1.3393 -2.24% 2. TIMELESS SOFTWARE 0.8368 -1.25% 3. TRANSPORT INTL. HLD. 0.5022 -0.04% 4. TYSAN HOLDINGS 0.9366 1.64% 5. UNIVERSE INTL. HLD. 1.2298 -0.24% Transport International Holdings has the second highest average return, while AcrossAsia has the least average monthly return of -2.24% among the five selected companies for the period between 1st January, 2001 and 1st December, 2013. The risk-return matrix of the five selected companies is as illustrated in table 4 below. Table 4: Risk-Return Matrix     Based on Mean Security Return (Mean = - 0.42)       High Low Total Based on Mean Security Risk (Beta) Mean = 0.9689 High Universe Intl. Hld. AcrossAsia 2 Low Transport Intl. Hld. & Tysan Holdings Timeless Software 3   Total 3 2 5     Based on Market Index Return = 0.41       High Low Total Based on Market Risk (Beta = 1) High - AcrossAsia & Universe Intl. Hld. 2 Low Tysan Holdings Timeless Software & Transport Intl. Hld. 3   Total 1 4 5 As indicated in table 4, based on the mean security return and mean security risk, Universe International Holdings investment portfolio is classified as a high risk-high return stock, while AcrossAsia is classified as a high risk-low return investment portfolio. On the other hand, Transport International Holdings and Tysan Holdings are both classified as low risk-high return investment portfolios, while Timeless Software is classified as a low risk-low return investment portfolio. Similarly as indicated also in table 4 above, based on the market index return and market risk, AcrossAsia and Universe International Holdings are both classified as high risk-low return investment portfolios, while Tysan Holding is classified as a low risk-high return investment portfolio. Timeless Software and Transport International Holdings on the other hand are both classified as low risk-low return investment portfolios. However, based on the market index return and market risk (Beta = 1), none of the five selected companies listed in the Hong Kong stock market can be classified as a high risk-high return investment portfolio. Discussion The main objective of the study was to identify and evaluate the relationship between beta and returns of investment portfolios. To attain this objective, the beta values and average return, was derived for the five selected companies listed in the Hong Kong stock market. Nevertheless, wide assumptions that relate to the financial market were not made, since the case study focused mainly on the beta-return relationship. Using the CAPM model, the beta of the respective five selected companies was established. In addition, the average monthly returns of each of the five selected investment portfolios were also determined. Consequently, it was established that AcrossAsia investment portfolio has the highest beta value of approximately 1.3393, while Transport International Holdings has the lowest beta value of approximately 0.5022. This implies that based on the beta values, AcrossAsia is the most volatile stock, while Transport International Holdings is the least volatile among the stocks of the five selected companies. Furthermore, of the five selected companies, AcrossAsia and Universe International Holdings had beta values of 1.3393 and 1.2298 respectively. The beta values of the two companies are higher than that of the market (Beta=1). This implies that the volatility of the two stocks is higher than the market volatility. Therefore, the risk associated with investing in AcrossAsia and Universe International Holdings is relatively high. This is because investment portfolios with beta values greater than one are more volatile and have a higher risk compared to portfolios with beta values of less than one. On the other hand, the other three companies of the selected five companies had beta values of less than one. The three companies included Timeless Software, Transport International Holdings and Tysan Holdings, which had beta values of 0.8368, 0.5022 and 0.9366 respectively. As established, the beta values of the three companies are less than that of the market (Beta=1). This indicates that the volatility of the three stocks is less than the market volatility of the Hong Kong stock exchange market. Typically, an investment portfolio with a beta value equal to one has the same volatility with that of the market. Therefore, the returns of such an investment portfolio changes with that of the market. Similarly, the average return of the respective five companies was determined. The average return relates to the period from 1st January, 2001 to 1st December, 2013. During this period the average market monthly return in the Hong Kong stock exchange market was 0.41%. In addition, among the five selected companies Tysan Holdings had the highest average return of 1.64%, while AcrossAsia had the lowest average return of -2.24%. Furthermore, among five selected companies, Tysan Holdings is the only company with a positive average monthly return. The other four companies which included AcrossAsia, Timeless Software, Transport International Holdings and Universe International Holdings had a negative average return during the same period. To evaluate the beta-return relationship of the five selected companies listed in the Hong Kong stock exchange market, the risk-return matrix was used. Based on the mean security return and mean security risk, Universe International Holdings investment portfolio was classified as a high risk-high return stock, while AcrossAsia was classified as a high risk-low return investment portfolio. This is because the beta values of the two stocks were higher than the equally weighted average beta of the five selected companies. However, the average return of Universe International Holdings was higher than the equally weighted average return of the five stocks, while AcrossAsia had a lower average return than the equally weighted average return of the selected five stocks. Similarly, Transport International Holdings and Tysan Holdings were both classified as low risk-high return investment portfolios, while Timeless Software was classified as a low risk-low return investment portfolio. However, based on the market index return and market risk, AcrossAsia and Universe International Holdings were both classified as high risk-low return investment portfolios, since the beta of the two companies was greater than that of the market (Beta=1), but their average returns were lower than the average market index return. Tysan Holding was classified as a low risk-high return investment portfolio, while Timeless Software and Transport International Holdings were both classified as low risk-low return investment portfolios. However, based on the mean market index return and market risk (Beta = 1), none of the five selected companies listed in the Hong Kong stock market was classified as a high risk-high return investment portfolio. Conclusion The sample data from the Hong Kong stock market used in this study was quite insightful in providing information related to beta-return relationship. Typically, the investment portfolios with low beta values tend to have lower returns than those with high beta values. However, there are exceptional scenarios where an investment portfolio can have low beta value but relatively higher returns. Such cases illustrate the stability of the investment portfolio. Similarly, an investment portfolio could have a beta value of greater than one, but with relatively lower returns compared to other investment portfolios over a long term period. According to the findings of this case study, AcrossAsia is the most volatile stock of the five selected companies since it has the highest beta value that is greater than one. However, the average return of AcrossAsia investment portfolio is also the lowest compared to the average returns of the other four companies. On the other hand, Transport International Holdings had the lowest beta value that is less than that of the market, implying that the stock is the least volatile among the five selected companies. However, the average return of Transport International Holdings is higher than that of AcrossAsia and Universe International Holdings which are the two stocks perceived to be the most volatile among the selected five companies. This indicates that over a long term period, an investment portfolio with a higher beta value that is greater than that of the market (Beta=1) tend to have lower returns compared to an investment portfolio with a lower beta value. Reference list Brailsford, T, Reaney R, Bilson, C 2004, Investments: concepts and applications, 2nd edition, Thomson. Haugen, R., 2012, Case closed: High volatile stocks have lower returns, robeco.com, May, 16. Hallerbach, G.W., 2003, Holding Period Return-Risk Modelling: Ambiguity in Estimation. Horcher, K. A., 2005, Essentials of financial risk management. John Wiley & Sons. Ilmanen, A., 2011, Expected Returns: An Investor's Guide to Harvesting Market Rewards. John Wiley & Sons. McNeil, A. J., Frey, R., & Embrechts, P., 2005, Quantitative risk management: concepts, techniques and tools. Princeton University Press. Shim, J.K. & Siegel, J.G., 2008, Financial Management, Barron's Educational Series. Tofallis, C., 2008, Investment Volatility: A Critique of Standard Beta Estimation and a Simple Way Forward. European Journal of Operational Research 187 (3): 1358–1367. Read More