Beta Management Company.

University Degree Business and Administrative studies

IPMI Business School

Financial Management Case Done by Yan Sugondo

Regular Class of January 2003

Beta Management Company

Introduction

Sarah Wolfe of Beta Management Company, a small investment company near Boston, decided to expand her business after acquiring the clientele and assets she needed. In 1990, she had been successful in the management of Beta’s funds by focusing on the Vanguard Index 500 Trust, even generating good returns in the worst of times. After doubling the size of Beta, she decided to pick some smaller stocks to go along with the index mutual fund. She also planned to increase the proportion of Beta’s assets in equities, sensing that 1991 was going to be a good year.

Problem

In order to accomplish her goals, she had a choice between two small NYSE-listed companies, i.e. California R.E.I.T. and Brown Group, Inc. She felt both stocks had their ups and downs, but seemed like attractive investments. While always promising her clients to keep their exposure to risk at a minimum, she was faced with the dilemma of which stock to choose to increase her equity to $20 million. She was willing to spend $200,000 to begin her program, but she was concerned about the stock market’s inconsistency and exposing her clients to risks associated with the stocks.

Analysis

Table 1 : Variability of Stock Returns

Standard deviation is the square root of the variance and provides an estimation of the distance away from the mean for a group of variables. Knowing a stock’s standard deviation is important since it describes the stock’s variability in rate of return. Therefore, the riskiness of a stock can be determined by comparing its standard deviation to the standard deviation of other assets.

The standard deviation of the Vanguard 500, California REIT, Brown Group was calculated to be 4.61%, 9.23%, and 8.17% (using Excel spreadsheet), respectively. As expected, these results indicate that the two stocks carry more risk than the Vanguard 500 due to their larger standard deviation. Between the two stocks, Cal REIT carries the most risk because its standard deviation is greater than that of Brown Group. However, it is important to note that the statistical significance on all the values calculated was not determined, therefore the level of certainty for these results is not known.

In order to determine the variability of a portfolio of stocks the following formula is used:

Sp = [f2s2 + 2f(1-f) COV1,2 + (1-f)2s2]1/2

In this formula S is the standard deviation and S1,2 is the covariance between asset 1 and asset 2. The significance of covariance comes from whether its value is + or -, not its value. It describes whether two data sets are moving in the same direction or in different directions. If the covariance is positive, then the variables have co-movement and move in the same direction. If the covariance is negative, then the variables have inverse movement and ...

This is a preview of the whole essay

In order to determine the variability of a portfolio of stocks the following formula is used:

Sp = [f2s2 + 2f(1-f) COV1,2 + (1-f)2s2]1/2

The covariance, correlation coefficient and R Squared value between the Vanguard 500 and each of the stocks was calculated using formulas in Excel. The results are in the following table :

Table 2: Statistical Measures of Each Portfolio

In order to analyze the variability of a portfolio created with the Vanguard 500 and a stock, it is necessary to calculate the covariance between the Vanguard 500 and each of the stocks. The covariance between the Vanguard 500 and each of the stocks is positive indicating that the two stocks generally move in the same direction as the Vanguard 500.

To calculate the variability of the two portfolios created with 99% of the Vanguard 500 and 1% of either Cal REIT or Brown Group, the following calculations were performed:

For the 99% Vanguard 500 and 1% Cal. REIT portfolio the variability or standard deviation is calculated as follows: = [(0.99)2(0.0461)2 + 2(0.99)(0.01)(0.0003) + (0.01)2(0.0923)2]½ = 4.57 %

For the 99% Vanguard 500 and 1% Brown Group portfolio the variability or standard deviation is calculated as follows: = [(0.99)2(0.0461)2 + 2(0.99)(0.01)(0.0024) + (0.01)2(0.0817)2]½ = 4.61 %

In analyzing the variability of the portfolios containing 99% of the Vanguard 500 and 1% of either the Brown Group or Cal REIT, the portfolio with the Brown Group was calculated to have more variability. By combining the Vanguard 500 with the Brown Group the variability of the Vanguard 500 remained the same while the variability of the Brown Group drastically decreased. On the other hand, when the Vanguard 500 is combined with Cal REIT to form a portfolio, the variability of both assets decreases.

The result of the portfolio with the Brown Group having more variability than that of Cal REIT is interesting since Cal REIT has a higher standard deviation than Brown Group. However, the variability in a portfolio of assets is largely influenced by the covariance between the assets. The purpose of creating a portfolio of stocks is to generate a desirable level of expected return while attempting to reduce the amount of risk it carries. In order to achieve such a goal, assets selected for the portfolio should not have strong positive correlations. It is important to note that the significance of covariance comes from whether its value is + or -, not its value. Therefore, in order to assess the strength of association between the Vanguard 500 and each of the stocks it was necessary calculate correlation coefficient.

The correlation coefficient is a measure of association and provides a measure to the degree of linear association between two random variables. If the correlation coefficient is 1, then there is perfect positive correlation between the variables and they move in the same direction. If the correlation coefficient is -1, then there is perfect negative correlation between the variables and they move in opposite directions. If the correlation coefficient is 0, the there is no correlation between the variables.

The correlation coefficient between the Vanguard 500 and the Brown Group stock is positive and almost 10 times greater than the correlation coefficient between the Vanguard 500 and the Cal REIT stock. Since the correlation coefficient between the Vanguard 500 and the Brown Group is greater, its portfolio generates more risk than the Vanguard 500 and Cal REIT portfolio.

The R Squared value for each stock was also calculated to determine how the variation in rate of return of each stock is explained by the variation in rate of return of the Vanguard 500. R squared conveys the percent of variation in the dependent variable that is explained by variation in the independent variable. As such, R squared measures the percent of the total investment risk of each stock that is systematic risk and not diversifiable when combined with a market portfolio.

The Vanguard 500 and Brown Group has a higher R squared value indicting that 43% of the variance in the Brown Group’s rate of return is affected by the variance in the rate of return of the Vanguard 500. On the other hand, the Vanguard 500 and Cal REIT had very low R squared value (0.5%) revealing that the variance in the rate of return of Cal REIT is minimally affected by the variance in the Vanguard 500’s rate of return. These results also support the conclusion of the Vanguard 500 and Cal REIT portfolio being less risky.

A stock’s Beta provides a proportional measure of the sensitivity of the stock’s rate of return to the rate of return for the market portfolio. If Beta equals 1, then the stock has the same risk as the market portfolio and increases and decreases similarly as the market portfolio. If Beta is greater than one, then the stock’s systematic risk is greater than the market portfolio’s since the asset increases or decreases more in comparison to the market portfolio. If Beta is less than one, then the stock’s systematic risk is less than the market portfolio’s and increases or decreases less in comparison to the market portfolio. The Beta for the stocks was calculated using the following formula:

ß = Covariance (Stock, Vanguard 500) / Variance Vanguard 500

Table 3: Beta of Stocks

In this case, Brown Group (1.11) had a higher Beta than Cal REIT (0.14). These results are consistent with results analyzing the variability of each portfolio. In relation to the Vanguard 500, Cal REIT had a smaller correlation coefficient and R Squared value than Brown Group. Therefore, combining the Vanguard 500 and Cal REIT stock to create a portfolio will generate a smaller Beta value and less risk for an investor than a portfolio combining the Vanguard 500 and Brown Group.

Recommendation

Although the Brown Group stock has a smaller standard deviation than the Cal REIT stock, a portfolio consisting of the Brown Group stock and the Vanguard 500 has more variability than a portfolio consisting of the Cal REIT stock and the Vanguard 500. This result demonstrates that not only can individual stock or systematic risk be diversified when combined with a market portfolio, but also that diversification is more effective with two assets combined with correlation coefficients further away from 1.