 Study
 Slides
 Videos
3.1 Volatility
Of all the ways to describe risk, the simplest and possibly most accurate is “the uncertainty of a future outcome”. The anticipated return for some future period is known as the expected return. The actual return over some past period is known as the realized return. The simple fact that dominates investing is that the realized return on an asset with any risk attached to it may be different from what was expected. Volatility may be described as the range of movement (or price fluctuation) from the expected level of return. For example, the more a stock goes up and down in price, the more volatile that stock is. Because wide price swings create more uncertainty of an eventual outcome, increased volatility can be equated with increased risk. Being able to measure and determine the past volatility of a security is important in that it provides some insight into the riskiness of that security as an investment.
3.2 Standard Deviation
The most useful method for calculating the variability is the standard deviation and variance. Risk arises out of variability. If we compare the stocks of CompanyA and CompanyB in the table below, we find that the expected returns for both the companies are same but the spread is not the same. Company A is riskier than CompanyB because returns at any particular time are uncertain with respect to its stock.
The average stock for CompanyA and B is 12 but appears riskier than B as future outcomes are to be considered.

Company A 
Company B 
Expected Return 
12 
11 

16 
12 

4 
13 

20 
10 

8 
14 

Total=60 
Total=60 
Arithmetic Mean 
60/5=12 
60/5=12 
Stocks of CompanyA and CompanyB have identical expected average returns. But the spread is different. The range in CompanyA is from 8 to 12 and for CompanyB it ranges between 9 and 11 only. The range does not imply greater risk. The spread or dispersion can be measured by standard deviation.
Calculation of Standard Deviation
Company A
Possible Outcome 
Return (R) 
Probability (K) 
Weighted (R*K) 
Deviation (RE1) 
Deviation Squared (RE1)^2 
Weighted Deviation Squared k(RE1)^2 
1 
0.04 (4%) 
0.25 
0.010 
0.075 
0.005625 
0.001406 
2 
0.12 (12%) 
0.50 
0.060 
0.005 
0.000025 
0.000013 
3 
0.18 (18%) 
0.25 
0.045 
0.065 
0.004225 
0.001056 



0.115 


Total=0.002475 
Company B
Possible Outcome 
Return (R) 
Probability (K) 
Weighted (R*K) 
Deviation (RE1) 
Deviation Squared (RE1)^2 
Weighted Deviation Squared k(RE1)^2 
1 
0.05 (5)% 
0.25 
0.0125 
0.040 
0.001600 
0.000400 
2 
0.09 (9%) 
0.50 
0.0450 
0.000 
0.000000 
0.000000 
3 
0.13 (13%) 
0.25 
0.0325 
0.040 
0.001600 
0.000400 



0.090 


Total=0.000800 
Expected Return (E1)= Total of Weighted = 0.115= 11.5%
Standard Deviation = θ=√k(RE1)^2 = 0.049 or 4.9%
Expected Return (E1)= Total of Weighted = 0.090= 9%
Standard Deviation = θ= √k(RE1)^2 = 0.028 or 2.8%
Comparison of return and risk for stocks of CompanyA and CompanyB with standard deviation 4.9% of CompanyA and 2.8% of CompanyB
The standard deviations and probability distributions show that stock of CompanyA has a higher expected return and a higher level of risk as measured by standard deviation.
Standard deviation measures risk for both individual assets and for portfolios. It measures the total variation of return from expected return.
3.3 Beta
Beta is a measure of a security’s or portfolio’s volatility, or systematic risk, in comparison to the market as a whole. It is also known as “beta coefficient.”
The beta coefficient, in terms of finance and investing, describes how the expected return of a stock or portfolio is correlated to the return of the financial market as a whole. An asset with a beta of 0 means that its price is not at all correlated with the market; that asset is independent. A positive beta means that the asset generally follows the market. A negative beta shows that the asset inversely follows the market; the asset generally decreases in value if the market goes up.
Correlations are evident between companies within the same industry, or even within the same asset class (such as equities). This correlated risk, measured by Beta, creates almost all of the risk in a diversified portfolio. Thus, It measures the part of the asset’s statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio. Beta can be estimated for individual companies using regression analysis against a stock market index.
Beta is calculated using regression analysis, and you can think of beta as the tendency of a security’s returns to respond to swings in the market. A beta of 1 indicates that the security’s price will move with the market. A beta less than 1 means that the security will be less volatile than the market. A beta greater than 1 indicates that the security’s price will be more volatile than the market. For example, if a stock’s beta is 1.2 it’s theoretically 20% more volatile than the market. Many utilities stocks have a beta of less than 1. Conversely most hightech based stocks have a beta greater than 1, offering the possibility of a higher rate of return but also posing more risk.
By definition, the market itself has an underlying beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market (for simplicity purposes, the Nifty 50 is usually used as a proxy for the market as a whole). A stock that swings more than the market (i.e. more volatile) over time has a beta whose absolute value is above 1.0. If a stock moves less than the market, the absolute value of the stock’s beta is less than 1.0.
More specifically, a stock that has a beta of 2 follows the market in an overall decline or growth, but does so by a factor of 2; meaning when the market has an overall decline of 3% a stock with a beta of 2 will fall 6%. (Betas can also be negative, meaning the stock moves in the opposite direction of the market: a stock with a beta of 3 would decline 9% when the market goes up 3% and conversely would climb 9% if the market fell by 3%.)
Higherbeta stocks mean greater volatility and are therefore considered to be riskier, but are in turn supposed to provide a potential for higher returns; lowbeta stocks pose less risk but also lower returns. In the same way a stock’s beta shows its relation to market shifts, it also is used as an indicator for required Returns on Investment (ROI). If the market with a beta of 1 has an expected return increase of 8%, a stock with a beta of 1.5 should increase return by 12%.
As discussed in previous modules Expected return on equity, or equivalently, a firm’s cost of equity, can be estimated using the Capital Asset Pricing Model (CAPM). According to the model, the expected return on equity is a function of a firm’s equity beta (β) which, in turn, is a function of both leverage and asset risk (β):
where:
K_{E} = firm’s cost of equity
R_{F} = riskfree rate (the rate of return on a “risk free investment”, e.g. Govt Treasury Bonds)
R_{M} = return on the market portfolio
and Firm Value (V) = Debt Value (D) + Equity Value (E)
3.4 Alpha
Alpha is a riskadjusted measure of the socalled active return on an investment. It is a common measure of assessing an active manager’s performance as it is the return in excess of a benchmark index. Note that the term “active return” refers to the return over a specified benchmark (e.g. the Nifty 50), whereas “excess return” refers specifically to the return over the riskfree rate. It is a common error to confound these two terms, and the reader is cautioned to make a careful distinction between them when studying or discussing investments.
The difference between the fair and actually expected rates of return on a stock is called the stock’s alpha.
Alpha = R – R_{f –}beta (R_{m}R_{f})
where:
 Rrepresents the portfolio return
 R_{f}represents the riskfree rate of return
 Beta represents the systematic risk of a portfolio
 R_{m }represents the market return, per a benchmark
For example, assuming that the actual return of the fund is 30, the riskfree rate is 8%, beta is 1.1, and the benchmark index return is 20%, alpha is calculated as:
Alpha = (0.300.08) – 1.1 (0.200.08)
= 0.088 or 8.8%
The result shows that the investment in this example outperformed the benchmark index by 8.8%.
The key distinction between investing in alpha and beta equities is one of purpose. While they are both risk indicators, they are employed for different purposes. Alpha refers to the degree to which a stock’s return compares to a specified benchmark, and is thus more focused on the direct benefits of investing. Beta, on the other hand, is a measure of a stock’s systematic risk or volatility.