Capital Asset pricing model has a very important place in valuation, it helps us to find cost of equity for the valuation. The model has 3 inputs risk free rate, equity risk premium and beta, in this article we will talk about beta, its importance and how its calculated.
Risk is deviation of returns from expectations, financial theories have long taught us that high risk is always equals to high returns, but are all risk compensated? In fact, its only systematic risk that cannot be diversified is what is compensated.
Risk & Return models
There are several accepted risk return models in finance and they all share some common views about risk:
They all determine risk in terms of variance in actual returns around expectations, thus risk free investment is one that has equal expected and actual return
They measure risk from the perspective of marginal investors that are well diversified.
This makes risk models to break into 2 components: firm specific risk that are related only to a particular company or sector, and market component contain risk that cannot be diversified and this market risk should be rewarded.
The beta is one of the most important but elusive parameters in finance. According to the CAPM, it is a measure of the so-called systematic risk.
CAPM with assumptions about no transaction cost or private information, concludes that marginal investors hold a portfolio that include every traded asset in the market and the risk of any investment is the risk it adds on this “ market portfolio”. Expected return model under CAPM:
Expected return = RF + ERP(Beta)
APM which is built on assumption that asset should be priced to prevent any arbitrage opportunity, concludes there can be multiple source of market risk and beta’s relative to each of these sources measure expected return.
Expected return = Rf + ∑B(Risk premium)
What is beta?
Beta as a measure of systematic risk has 2 basic characterstics:
It measures the risk added on to a diversified portfolio, rather than total risk. thus, its possible for a instrument to have high risk individually but low risk when analysed in terms of market risk.
Beta is a relative measure of risk and it is standardized to be around 1.
Beta of an asset can be calculated using regression of returns of any asset against the returns of index, representing the market portfolio over a reasonable time period. Where returns of asset represents Y variable and returns on market represents X variale.
Equation we get is : R = a + b*RM
The slope of regression “B” is beta, because it measure the risk added by the investment to index used as proxy to the market portfolio.
Problem with regression beta:
Index Problem: Regression beta depend heavenly on the index used to regress the beta but which index shall we use? , A local equity index can be used as proxy for market portfolio but it can raise problem of large company in a small equity market, example Nokia in Finland’s equity market. where Nokia accounted for around 90% of Finnish equity market, which meant that we were regressing Nokia with 90% of Nokia only.
Result, high beta close to 1 or high for Nokia and beta less than 1 for smaller riskier companies. This problem can be solved by looking at who the marginal investor are? A good idea is to look at the marginal investors stock holding in the company and where are they based. If marginal investor is domestic then we can use domestic index but if marginal investor is from US then use S&P500 and if marginal investor is global then use global index like MSCI global index.
Noise problem: Using MSCI or S&P500 we can solve problem of dominating companies in small index but their is a second issue is how far shall we go back?
The regression beta is noisy and the range we get is quite large, for eg - let say you got regression beta as 1.2 with a standard error of 0.5, beta can practically be 0.7 to 1.7 which is practically of no use in valuation. To reduce standard error we need to increase the number of observation.
Standard error = Standard deviation/√no. of observation.
Problem of firm changing overtime: Even if stock do not dominate the index and beta we got has low standard error, their is another problem with regression beta i.e they are based on historical data & firm change over time.
The regression beta reflect the firms character on average given the period of estimate rather than firm as it exist today.
Firms have 3 reasons to change:
a. They divest in existing business, invest in new business or acquire new firm. In this situation it changes the business mix and which change their beta.
b. They can change the financial leverage by adding or paying off debt, in addition such as payment of dividend and buyback can effect financial leverage.
c. Even if financial leverage or business mix don’t change they tend to grow overtime as they grow their operating structure change which change their beta.
Adjusted beta
As result of difference in period, return interval and index etc. different service often end up with different beta, most service adjust their beta towards 1. A similar model developed by bloomberg is:
Adjusted beta = Regression beta (0.67) + 1(0.33)
Effectively pushing beta towards 1
but why adjust beta towards 1? The rationale is that overtime their is a tendency on part of beta of all companies to move towards one, Practically this should not come as a surprise as firms that survive in the market tend to grow and increase in size, overtime becoming more diversified and have more assets in place to produce cash flows. All this pushes the beta towards 1.
I have shared my own work on how to calculate regression beta on excel:
Bottom up Beta
Beta of a firm is determined by the fundamental decisions that firm takes on where to invest, what type of cost structure it plans to maintain and how much debt it takes on. Bottom up beta considers this factors in estimate of companies equity beta.
Lets first understand the fundamental that determine beta.
Type of business
Degree of operating leverage
Degree of financial leverage
Type of business: Since beta measure risk of firm relative to market index, the more sensitive a business is to market condition, higher the beta. Thus other things being equal a cyclical company will be expected to have a higher beta than non cyclical.
Building upon this point, we will also point that the degree to which firm’s products are discretionary or not will effect its beta. thus we can say beta of a cereal manufacturer will be low than beta of car manufacturer.
Firms generally have limited control over how discretionary their product or service that they provide to customer. Their are firms that have used this limited control to position their products as less discretionary to buyer and lower business risk. One approach is to make product integral and necessary to part of everyday life, thus making its purchase more a requirement. eg, blinkit e-commerce business positioning. Second approach is to effectively use advertisement and marketing to build brand loyalty.
Degree of operating leverage: Degree of operating leverage is function of cost structure of a firm and its usually defined in terms of relations between fix cost and total cost.
Generally firms with higher operating leverage will have a higher variability in earnings than a similar firm with lower operating leverage. thus, higher operating leverage will lead to a higher beta.
While operating leverage do affect a companies beta, it is difficult to measure operating leverage of a firm from outside since fix cost and variable cost bifurcation is not provided by companies.
An approximate approach to measure operating leverage is :
% change in operating income/%change in sales
Degree of financial leverage: Other things being equal increase in financial leverage lead to increase in equity beta. As obligated payment on debt increase the volatility in net income, with higher leverage increasing income in good times and reduce at bad times.
BL = Bu ( 1+(1-T)*(D/E))
Unlevered beta is determined by the type of business it operate and operating leverage, then equity beta is determined by riskiness of business, operating leverage and financial leverage.
Breaking bottom up beta into business risk, operating leverage and financial leverage help us with an alternative way of estimating beta.
#Steps in calculating bottom up beta:
Identify the business or businesses that make up the firm.
Estimate the unlevered beta for the business or businesses that firm is involved, the simplest approach uses those unlevered beta directly without adjusting for any difference between the firm being analyse and average firm in the sector.
Calculate unlevered beta for firm, take average of unlevered beta of firms being analysed
Calculate the leverage of the firm using market value if available, if not use target leverage specified by management or industries typically debt ratios
Estimate levered beta for the firm. using unlevered beta of firm from step 3 and leverage of firm from step 4.
Their are 3 reasons this beta is better estimate than regression.
We calculate unlevered beta by sector with average across regression beta, while regression beta can be noisy & have higher standard error, average across regression beta can reduce the noise in estimation.
Beta reflects the firm as it exist today, since it is computed based upon current weights for different business. In fact changes in business mix is easily reflected in bottom up beta.
Finally levered beta is calculated using current leverage of the firm, rather than average leverage over the period of time.
I have provided my own bottom up beta calculation below, do check out.