Question

Please provide a depth satisfactory analysis (around 300 words) of why the standard deviation , coefficient of variation, CAPM, beta exercises are not sufficient to make a sound investment decision. The discussion may refer to deficiencies in the models utilized, unrealistic assumptions, theoretical shortcomings, etc. note : address new knowledge that was not covered in the book of PRINCIPLES OF FINANCIAL MANAGEMENT .

Answer 1

Standard deviation is a basic mathematical concept that measures volatility in the market, or the average amount by which individual data points differ from the mean. Simply put, standard deviation helps determine the spread of asset prices from their average price.

When prices swing up or down, the standard deviation is high meaning there is high volatility. On the other hand, when there is a narrow spread between trading ranges, the standard deviation is low, meaning volatility is low. What can we determine by this? Volatile prices mean standard deviation is high, and it is low when prices are relatively calm and not subject to wild swings.

Risk measurement is a very big component of many sectors of the finance industry. While it plays a role in economics and accounting, the impact of accurate or faulty risk measurement is most clearly illustrated in the investment sector.

1.            One of the most common methods of determining the risk an investment poses is standard deviation.

2.            Standard deviation helps determine market volatility or the spread of asset prices from their average price.

3.            When prices move wildly, standard deviation is high, meaning an investment will be risky.

4.            Low standard deviation means prices are calm, so investments come with low risk.

In investing, standard deviation is used as an indicator of market volatility and, therefore, of risk. The more unpredictable the price action and the wider the range, the greater the risk. Range-bound securities, or those that do not stray far from their means, are not considered a great risk. That's because it can be assumed with relative certainty that they continue to behave in the same way. A security with a very large trading range and a tendency to spike, reverse suddenly, or gap is much riskier, which can mean a larger loss. But remember, risk is not necessarily a bad thing in the investment world. The riskier the security, the greater potential it has for payout.

                 The coefficient of variation (COV) can determine the volatility of an investment. The COV is a ratio between the standard deviation of a data set to the expected mean. When used in the stock market, it helps to determine the amount of volatility in comparison to the expected return rate of investment. Dividing the volatility, or risk, by the absolute value of the investment's expected return, determines the COV.

The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population. In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. Ideally, the coefficient of variation formula should result in a lower ratio of the standard deviation to mean return, meaning the better risk-return trade-off. Note that if the expected return in the denominator is negative or zero, the coefficient of variation could be misleading.

The coefficient of variation is helpful when using the risk/reward ratio to select investments. For e.g. An investor who is risk-averse may want to consider assets with a historically low degree of volatility and a high degree of return, in relation to the overall market or its industry. Conversely, risk-seeking investors may look to invest in assets with a historically high degree of volatility.

1.            The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean.

2.            In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments.

3.            The lower the ratio of the standard deviation to mean return, the better risk-return trade-off.

                                       The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital.

Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula accounts for the time value of money. The other components of the CAPM formula account for the investor taking on additional risk.

The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.

A stock’s beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset.

The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return.

There are several assumptions behind the CAPM formula that have been shown not to hold in reality. Modern financial theory rests on two assumptions:

(1) Securities markets are very competitive and efficient (that is, relevant information about the companies is quickly and universally distributed and absorbed);

(2) These markets are dominated by rational, risk-averse investors, who seek to maximize satisfaction from returns on their investments.

Despite these issues, the CAPM formula is still widely used because it is simple and allows for easy comparisons of investment alternatives.

Including beta in the formula assumes that risk can be measured by a stock’s price volatility. However, price movements in both directions are not equally risky. The look-back period to determine a stock’s volatility is not standard because stock returns (and risk) are not normally distributed.

The CAPM also assumes that the risk-free rate will remain constant over the discounting period. Assume in the previous e.g. that the interest rate on U.S. Treasury bonds rose to 5% or 6% during the 10-year holding period. An increase in the risk-free rate also increases the cost of the capital used in the investment and could make the stock look overvalued.

The market portfolio that is used to find the market risk premium is only a theoretical value and is not an asset that can be purchased or invested in as an alternative to the stock. Most of the time, investors will use a major stock index, like the S&P 500, to substitute for the market, which is an imperfect comparison.

The most serious critique of the CAPM is the assumption that future cash flows can be estimated for the discounting process. If an investor could estimate the future return of a stock with a high level of accuracy, the CAPM would not be necessary.

Considering the critiques of the CAPM and the assumptions behind its use in portfolio construction, it might be difficult to see how it could be useful. However, using the CAPM as a tool to evaluate the reasonableness of future expectations or to conduct comparisons can still have some value.

Imagine an advisor who has proposed adding a stock to a portfolio with a $100 share price. The advisor uses the CAPM to justify the price with a discount rate of 13%. The advisor’s investment manager can take this information and compare it to the company’s past performance and its peers to see if a 13% return is a reasonable expectation.

Assume in this e.g. that the peer group’s performance over the last few years was a little better than 10% while this stock had consistently underperformed with 9% returns. The investment manager shouldn’t take the advisor’s recommendation without some justification for the increased expected return.

An investor can also use the concepts from the CAPM and efficient frontier to evaluate their portfolio or individual stock performance compared to the rest of the market. For e.g., assume that an investor’s portfolio has returned 10% per year for the last three years with a standard deviation of returns (risk) of 10%. However, the market averages have returned 10% for the last three years with a risk of 8%.

The investor could use this observation to reevaluate how their portfolio is constructed and which holdings may not be on the SML. This could explain why the investor’s portfolio is to the right of the CML. If the holdings that are either dragging on returns or have increased the portfolio’s risk disproportionately can be identified, the investor can make changes to improve returns.

The CAPM uses the principles of Modern Portfolio Theory to determine if a security is fairly valued. It relies on assumptions about investor behaviors, risk and return distributions, and market fundamentals that don’t match reality. However, the underlying concepts of CAPM and the associated efficient frontier can help investors understand the relationship between expected risk and reward as they make better decisions about adding securities to a portfolio.

                  Beta is a measure of the volatility or systematic risk–of a security or portfolio compared to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return, for assets (usually stocks). CAPM is widely used as a method for pricing risky securities and for generating estimates of the expected returns of assets, considering both the risk of those assets and the cost of capital.

1.            Beta, primarily used in the capital asset pricing model (CAPM), is a measure of the volatility–or systematic risk of a security or portfolio compared to the market as a whole.

2.            Beta data about an individual stock can only provide an investor with an approximation of how much risk the stock will add to a (presumably) diversified portfolio.

3.            For beta to be meaningful, the stock should be related to the benchmark that is used in the calculation.

A beta coefficient can measure the volatility of an individual stock compared to the systematic risk of the entire market. In statistical terms, beta represents the slope of the line through a regression of data points. In finance, each of these data points represents an individual stock's returns against those of the market as a whole.

Beta effectively describes the activity of a security's returns as it responds to swings in the market. A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's returns over a specified period.

The beta calculation is used to help investors understand whether a stock moves in the same direction as the rest of the market. It also provides insights about how volatile–or how risky–a stock is relative to the rest of the market. For beta to provide any useful insight, the market that is used as a benchmark should be related to the stock. For e.g., calculating a bond ETFs beta using the S&P 500 as the benchmark would not provide much helpful insight for an investor because bonds and stocks are too dissimilar.

Ultimately, an investor is using beta to try to gauge how much risk a stock is adding to a portfolio. While a stock that deviates very little from the market doesn’t add a lot of risk to a portfolio, it also doesn’t increase the potential for greater returns.

In order to make sure that a specific stock is being compared to the right benchmark, it should have a high R-squared value in relation to the benchmark. R-squared is a statistical measure that shows the percentage of a security's historical price movements that can be explained by movements in the benchmark index. When using beta to determine the degree of systematic risk, a security with a high R-squared value, in relation to its benchmark, would increase the accuracy of the beta measurement.