CHAPTER 8
RISK AND RETURN
Risk in investment and decision analysis refers to the lack of knowledge about the exact outcome in future of a decision taken now, even though the possible outcomes are known with their likelihoods of occurrence. Making the decision now usually has a cost (cash outflow) with possible benefits (cash inflows
or % Returns) in future period(s). Since the cost is incurred now, it is known with certainty. The future benefits (dollar amounts or % Returns) have to be forecasted and may depend on external influences. Since risk carries the possibility of a real or opportunity loss, investors are averse to it, but, as the saying goes, no pain no gain. Therefore investors are willing to take risk, as long as the reward (expected return) is commensurate with the risk (required return). As we learned in earlier chapters, in equilibrium the required return should be equal to the expected return.
The assumptions in the following discussion are:
1. The investor/decision maker is rational
2. The investor/decision maker is risk-averse, i.e., does not like risk, but is willing to take it, requiring a higher return for assuming a higher level of risk and a lower return for assuming a lower level of risk.
The investment decision itself may be of two types:
1. Stand-alone investment: all the money is invested in one asset picked as
the best in a risk-return framework from a set of available assets or
investment opportunities. In this case, the risk is all the risk of the
selected asset and is called stand-alone (total) risk of the asset
2. Investment in a portfolio context: only a part of the available money is
invested in a particular asset, other assets picking up the remainder of
money. Thus, the investment money is allocated to more than one asset
and we are said to have a portfolio (of assets). In this case the risk to be
considered is the portfolio risk of the asset, i.e., what risk does a particular
asset bring to the portfolio
Since investors are risk averse and desire to lower risk through diversification, i.e., investing in a portfolio of assets, making investment decisions in a portfolio context is the sensible thing and therefore we will focus on this type of investment.
The risk of a single asset, the Stand-alone risk, has two components:
1. A component associated with macroeconomic or market-wide events and it is non-diversifiable, i.e., it cannot be eliminated even after proper diversification. It is also called systematic risk.
2. A component associated with asset-specific (industry specific) events and it is diversifiable, i.e., it can be eliminated through proper diversification. This component is also called unsystematic risk.
Therefore, in the final analysis of risk and return, it is the non-diversifiable risk that is relevant for requiring return. This risk is measured by a statistic called beta.
A beta of 1 represents average non-diversifiable, systematic risk. A large, well-diversified portfolio, called the Market Portfolio (e.g. the S&P 500 Index) has a beta of 1.
A beta 1 represents above average non-diversifiable, systematic risk
A beta 1 represents average non-diversifiable, systematic risk
A beta =0 represents a risk-free asset (e.g. T-Bill)
There is a model called the Capital Asset Pricing Model (CAPM), which is also called the Security Market Line (SML) which relates the required rate of return of an asset and its systematic, non-diversifiable risk measured by beta. It is as follows:
ri = rRF + [(rM - rRF) * bi]
where
ri = Required Rate of Return for the ith
Investment
rRF = Risk-Free Rate of Return (say, U.S. T-Bill)
rM = Required Rate of Return on the market
Portfolio (say, the S&P 500 Index)
rM - rRF = the risk-premium for assuming average
systematic risk
bi = Beta of the Investment
FOR EXAMPLE, IF AN ASSET, SAY THE COMMON STOCK OF A COMPANY), HAS A BETA OF 1.5 AND THE RISK-FREE RATE OF RETURN IS 5% AND THE REQUIRED RETURN ON THE MARKET PORTFOLIO IS 15%, THE REQUIRED RETURN ON THE COMMON STOCK IN QUESTION WOULD BE
= 5 + [(15-5)*1.5]
= 5 + [10*1.5]
= 5+15 = 20%
STEPS IN MAKING PORTFOLIO INVESTMENT IN A RISK-RETURN FRAMEWORK
1. FIND THE BETA OF THE INVESTMENT
2. FIND THE RISK-FREE RATE OF RETURN (T-Bill Rate)
3. FIND THE RATE OF RETURN ON THE MARKET PORTFOLIO (RATE ON S&P 500 INDEX)
4. APPLY THE CAPM/SML TO FIND THE REQUIRED RATE OF RETURN ri :
ri = rRF + (rM - rRF) * bi
where
ri = Required Rate of Return for the ith
Investment
rRF = Risk-Free Rate of Return (say, U.S. T-Bill)
rM = Required Rate of Return on the market
Portfolio (say, the S&P 500 Index)
bi = Beta of the Investment
5. FIND THE EXPECTED RATE OF RETURN OF THE
^
INVESTMENT ri
6. COMPARE THE REQUIRED RATE OF RETURN
AND THE EXPECTED RATE OF RETURN TO SEE
WHETHER THE INVESTMENT IS FAIRLY
PRICED,UNDERPRICED OR OVERPRICED AND
MAKE THE APPROPRIATE INVESTMENT
DECISION