# Measuring The Risk Of Equity Shares

- Risk is an integral part of equity investment, making it important to understand and measure risk of an equity share.
- Value investors judge the riskiness of a stock by looking at the fundamentals and current price levels of the stock.
- Statistically, risk of a stock is measured by deviation of a stock returns from its mean or the market.

The Oxford English dictionary defines risk as “A situation involving exposure to danger”. However in finance risk and return go hand in hand. The Chinese symbol of risk better explains the risk involved in finance. In fact, the Chinese Symbol of risk is nothing but a combination of Danger and Opportunity symbols!

It is common belief that to generate higher returns you need to accept higher risk. A value investor like Warren Buffett would certainly disagree to this. A value investor aims to generate ‘safe and above average’ returns.

On the highly safe side, the treasury bills tend to generate lower returns over a long period of time. The treasury bonds which carry a higher degree of risk compared to treasury bills because of longer term to maturity, generate higher rate of return compared to treasury bills. The equity stocks which carry maximum risk, typically tend to generate maximum return over a longish period of time. The following table gives annualized returns for S&P 500, treasury bills and treasury bonds.

Period | S&P 500 |
3-month T. Bill |
10-year T. Bond |

1928-2013 | 9.55% | 3.53% | 4.93% |

1964-2013 | 9.89% | 5.07% | 6.56% |

2004-2013 | 7.34% | 1.54% | 4.27% |

(Source: http://pages.stern.nyu.edu)

The question is “how do we actually quantify or measure the risks associated with a stock?” There are various concepts developed over the last five decades which help in measuring risks associated with stocks. Broadly speaking there are two viewpoints concerning risk. The first, emphasized by value investors like Warrant Buffet, focuses on fundamentals and the management of the company. While the second approach, favorite of academia, is more statistical one. It measures the risk of stock based on fluctuations of its returns. We have summarized the statistical measures of risk below:

- Variance: It measures the fluctuation of stock returns from its average (mean). Higher the variance, riskier the stock. For example Groupon (GRPN), which has variance of more than 50% is a risky stock.
- Beta: It measures the riskiness of the stock in comparison with the market or the index. A stock having beta greater than one is riskier than the index while stock having beta lower than one carries less risk than index.
- VAR: It answers the question “what’s the maximum money I could lose?” It measures the downside deviation of stock returns.

We will have a more in depth look into these measures throughout the rest of this article. We have used Google (GOOGL), Groupon and Amazon (AMZN), in our article as illustrative examples.

## Variance as a measure of equity risk

Harry Markowitz in his path breaking paper “PORTFOLIO SELECTION” introduced the concept of variance as a measure of risk. In Markowitz “mean-variance” world, returns were measured by mean returns and risk by variance or its root, standard deviation (volatility), which measures how dispersed the returns of a stock is. Risk is defined as the probability that actual return may be different from expected return. Hence stocks having higher variance carry higher risk. Interestingly, variance doesn't differentiate between dispersion above the mean and dispersion below the mean. There is nothing called “good deviation” or “bad deviation”. All deviations are considered equally harmful.

Consider a stock, Stock A, whose price has consistently declined from $50 to $10, while there is another stock, Stock B, whose price has consistently appreciated from $10 to $50. Now which among the two stock is more risky? Obviously Stock A, right? No, if we take variance as measure of risk. Both have same variance and hence are equally risky.

Variance as a measure of risk can be associate with markets general attitude towards uncertainty. Higher fluctuation makes prediction of stock prices more difficult, increasing uncertainty and hence, risk. The annualized standard deviation of Google , Groupon , and Amazon for different time periods are given below. First, daily standard deviation based on daily prices is calculated. Daily standard deviation is annualized by multiplying it with square root of total number of trading days in a year.

One Year | Two years | Five Years | |

GOOGL | 23.61% | 21.78% | 24.51% |

GRPN | 58.89% | 70.49% | NA |

AMZN | 33.05% | 29.80% | 32.74% |

While Google is least risky across all time periods, Groupon is riskiest among the three. From the table it can also be seen that standard deviation of a stock varies depending on the time period chosen.

## Beta as a measure of equity risk

Beta or CAPM Beta as it is generally called, as a measure of risk was introduced by William Sharp, who won Nobel Prize for developing CAPM, Capital Asset Pricing Model. Essentially Sharpe, carrying on Markowitz arguments to logical conclusion, argues that only those risk which cannot be diversified should be rewarded. According to him all the risks associated with a stock are captured by a single number, beta. While variance measures the deviation of returns from the mean, beta measures the co-movement of a security in relation to the market, which generally is an index like S&P 500. A stock which moves in tandem with the market has beta of 1. A stock which has more variance than the market average has beta greater than one, conversely, a stock which has lesser variance than the market has beta lower than one.

S&P 500 | Stock A | Stock B |

1500 | 120 | 120 |

1650 (10% increase) | 138 (15% increase) | 126 (5% increase) |

1485 (10% decline) | 120 (13 % decline) | 116 (8% decline) |

In the above example Stock A has beta greater than one while Stock B has beta lower than one. Stocks having beta of one are riskier than the market while stocks having beta of less than one carry lesser risk the market. It is also possible to have negative beta if the returns on the stock and the market are negatively correlated. So, does a stock having higher variance also has higher beta? Not necessarily. A stock will have higher beta only if it adds extra risk to the market portfolio. Put simply, variance is comparison to self while beta is in comparison with the markets. Hence, a stock having high variance may have lower beta. Mathematically beta is covariance of the stock with the market divided by variance of the market.

β = Covariance (St,M)/Variance (M)

Where “St” is the stock returns and “M” is market returns.

Beta of google, Amazon (AMZN) and Groupon (GRPN) for different time periods is given in the following table.

One Year | Two years | Five Years | |

GOOGL | 1.38 | 1.12 | 0.95 |

GRPN | 1.66 | 1.41 | NA |

AMZN | 1.88 | 1.46 | 1.11 |

As can be seen from the table, beta of a stock varies considerably with the time period. Regression beta of a stock will differ with change in the time period (one year, two years, etc.), the time interval for which returns were measured (daily, weekly, etc.) and the index against which the stock returns were regressed (NASDAQ, S&P 500, etc.)

Beta, today is the most widely used measure of risk associated with a stock. However recent studies show that beta may not explain all the risk associated with the stock, in fact it may be very poorly correlated with risk (see Fama and French 1992). These studies also show that CAPM (which uses beta as a measure of risk) understates the return generated by low beta stocks and overstates the returns generated by high beta stocks.

## Value at Risk as a measure of equity risk

Value At Risk (VAR), is the new science of measuring risk. VAR quantifies the worst case scenario given the time period and confidence level. It tries to answer the question “what is the maximum loss I can suffer during the month?” The major difference between variance and VAR is that while variance does not differentiate between increases or decline in price, VAR tries to capture only the decline in price. In a way, for an investor, risk is about losing money, and VAR captures just that. VAR is generally used for measuring risk associated with a portfolio. There are three key elements in VAR, maximum level of loss in value, time horizon, and confidence level. Time horizon refers to the period for which VAR has to be computed, daily, monthly or yearly. Confidence level tell you how sure you can be. The confidence level refers to the percentage of all possible samples included in the population. It can be better explained with an example. When we say that 10 day VAR with Confidence level of 95% is $200,000, it implies that there is 5% chance of maximum loss exceeding $200,000. There are three different methods of calculating VAR.

**Historical Simulation method:**In this method historical returns from the security is arranged in ascending order with lowest returns at the beginning and highest at the end. The appropriate return value corresponding to the class interval is the VAR. VAR at 95% confidence level will be the return value at the fifth percentile.**Variance-Covariance method:**This method assumes normal distribution for stock returns and calculates VAR based on mean and standard deviation. Consider a very simple example. The mean price of the Stock A is $100 and standard deviation is $10. Then with 95% confidence we can say that price of the stock will not fall below $80 (for a normally distributed curve 95% of the observation falls within 2 standard deviation). This approach becomes complex if the number of assets in the portfolio increases as it also takes into account the covariance between price movements of different assets.**Monte Carlo simulation:**It is almost same as historical data simulation, the difference being the fact that returns data is randomly generated. Returns are not historical returns as is the case in historical data simulation method.

## Value Investor’s Definition of Risk

Variance, beta and value at risk are statistical measures, which depend on the variance, covariance and probability distribution of returns. These measures associate uncertainty of stock returns with risk. But value investors like Benjamin Graham and Warren Buffet disagree. They define risk as “permanent loss of capital”. They are not worried by the deviations in returns of a stock. What matters is the fundamentals and the management of the company. A value investor has a very long investment horizon. As Warren Buffett put it “our favorite holding period is forever”. Deviations in returns are just deviations, nothing much. One should not be overly concerned about them. As Warren Buffet has famously said “Only buy something that you'd be perfectly happy to hold if the market shut down for 10 years”. Value investor is not concerned about price variance but about the general price level of the stock. Any investment is risky at a high price. Value investors look for a margin of safety, intrinsic value of stock being considerably lower than its market price. In Oracle of Omaha’s words “It's far better to buy a wonderful company at a fair price than a fair company at a wonderful price”. A value investor sees risk in a company with sound financials and future prospects if its price is high. For a value investor a stock which sees very high fluctuations in its returns but is currently priced 15%-20% below its market price is less risky than a stock with stable prices but priced at par with its intrinsic value.

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