Estimation of Beta-Based Expected Returns
I use Beta-based expected return to calculate and understand potential capital appreciate (or cash flow) from a given stock.
In today’s post, I am discussing the concept of stock’s beta value and how it helps us understand stocks expected returns.
What is Stock’s Beta Value?
In its simplistic form, beta is a measure of any individual stock’s risk (or movement) relative to the overall stock market risk (or movement). I measure Beta of any given stock relative to the S&P CNX NIFTY. Here, I am trying to understand how a stock price behaves relative to the market and how to factor in the capital appreciation into my expected returns. We can calculate Beta either using daily return (i.e. daily pricing) or on monthly returns (monthly pricing). The results should be the same because it is the on relative basis.
How to calculate Beta?
The formula for calculating Beta is written as:
Beta = Covariance (stock vs. market) / Variance (market)
Let us take an example, where we want to calculate the Beta for daily returns (relative to market). We will calculate approximately 4 year Beta for NTPC. We will use a simple linear regression method that can be implemented using Microsoft’s Excel or Google’s spreadsheet. The excel model is available in my toolbox menu.
Step 1 (Column B):
Download S&P CNX NIFTY index daily value history from November 2004 to March 2009. Any other time is also acceptable.
Step 2 (Column C):
Download price history of any stock (in our example NTPC) from January 1998 to December 2008, i.e. using the same daily pricing as we used for index above. The site I use for pricing history is NSE stock exchange. Sort the data such that March 2009 gets aligned for both index and the stock pricing.
Step 3 (Column D):
Calculate the daily returns by (Cell B3 – Cell B2) / (Cell B2). Calculate this for the complete data set, In our case until November 2004. Column D will now have daily returns for index going back to November 2004.
Step 4 (Column E):
Similarly, calculate the daily returns for NTPC stock price in Column E.
Step 5 (Cell H4):
Calculating the Beta using the formula mentioned above.
= covariance (stock vs. market index returns) / variance (market index returns)
= COVAR(E3:E1095,$D$3:$D41095)/VARP($D$3:$D$1095)
= 0.67
Step 6: The Beta value for daily return for NTPC of 0.67.
What this means is the stock of NTPC returns 0.67 times the S&P CNX NIFTY index. It can also be interpreted as that volatility (or risk) of this stock is less than market index.
- Beta value greater than 1 – The stock’s price experiences movements that are greater (more volatile and/or more risk) than the stock market index.
- Beta value less than 1 – The stock’s price movements, or swings, are less than those of the stock market index.
- Beta value equal to 1 – The stock moves in tandem with the market
Now that we know the stock’s Beta value, it can used to calculate the expected return. This calculation is based on Capital Asset Pricing Model (CAPM). It uses risk-free investments, expectations of the stock market, and stock Beta values. While discussing CAPM is a topic in itself, here I am only showing the simple mathematical model. The expected return (ER) is calculated as:
ER = (risk free return) + (Beta) x (expected market return – risk free return)
Where:
- Risk free return – This is the interest rate one would get from government bonds. These returns are very low. Hence, I like to use high yielding savings/CDs available in the market. At this point in time, I am using 7% interest rate.
- Beta – it provides stock’s relationship with the market.
- Expected market return – It is the expected market return from a stock market indicator such as the S&P CNX NIFTY. Since 2000, I have estimated that S&P CNX NIFTY yielded average annual return of approximately 15.5%. I will continue to refine this matrix, as we make more progress this year. My personal viewpoint is this 15.5% is not sustainable. If I include data from 1990 onwards, this expected market return will come down. I am still pondering over the rationale to use a reduced value.
In our example for NTPC, expected return can be calculated as:
ER = 7.0% + 0.67 x (15.5% – 7.0%)
= 12.7%
What this means is, that the four year expected return for NTPC stock is 12.7%. What this shows is, with low risk/volatility relative to the market comes the stock’s low returns compared to the market.
Few important issues that we need to understand:
- This calculated expected return is not relative to individual investor’s investment. It is relative to the stock market index represented by S&P CNX NIFTY. The individual investor’s personal return will depend upon each individuals cost basis.
- This calculated expected return does not include returns due to dividends.
- This calculated expected return is based on the Beta calculated using past historical data. It may not reflect the future relative movements of stock vs. market index.
In future posts, I will discuss how individual investors can calculate (or develop simple model) a given stock’s return that includes dividend and beta-based expected returns. So stay tuned !
beta, expected returns
TIP Guy,
A nice and clear article with simple language as usual. I get to know the logic in calculating the beta value. But, I found few glitches in the example you have shown and I wish to get clarified.
First, as per your excel sheet, let the market index returns be the Nifty returns (column D) and stock be the NTPC returns (column E).
As per the beta formula, beta for NTPC will be as follows:
beta = covar(column E, column D) / var(column E)
But in your excel sheet, it was:
beta = covar(column D, column D) / var(column E)
If I make the above changes, the beta value for NTPC turns to be 0.67 and ER is just 13.5%
I am not trying to pinpoint you here, but just trying to ensure that I get your point correctly. Let me know if my above observation is right.
Please do continue your excellent work.
Silambu,
Thank you for pointing an error to me. I appreciate it. I have corrected the error in text and excel sheet. Beta = covar(column E, column D) / var(column D). Beta is 0.67 and ER is now 12.7.
TIP Guy,
a good article, which represented beta calculation for stock analysis. but friend i am unable to find the excel model as you linked in the toolbox. can sent the excel to my mail id or upload same in the toolbox
Hello Murali,
The excel model is available in the toolbox. I just checked. Also, I have emailed you a copy.
Best Wishes,
hi Tip Guy
Nice Model.
I am not well articulate in using Excel, so could you tell me that while calculating Co-variance what this “$” sign means =COVAR(E3:E1095,$D$3:$D$1095)/VARP($D$3:$D$1095)
Thanks
Hi Guys,
Can anyone let me know how to evaluate beat if standard deviation of A & B stocks is given, their correlation coefficient is also known, and portfolio standard deviation is also known?
Hi,
Its not actually Beat — its BETA!
why do you leave out dividends in beta calculation and if dividends were to be included how would that fit into into the formula
Hello Karl,
Very good observation! If I were to calculate beta for US company stock, then, yes, I would tend to think including dividends makes sense. In US, dividends are more predictable (if you think beyond the 2008/2009 dividend cuts). In emerging countries like India, two issues (1) it is difficult to include because they are not that uniform, it could be more or it could be less; and (2) generally, it is distributed only once in full year, this makes it insignificant – Yes I have tried calculating it, the difference is of the order of 0.001.
Best Wishes,
Could you please tell where we can get beta values of indian stocks
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