Chapter 5. Understanding Risk. Understanding Risk: The Big Questions. What is risk? How can we measure risk? What happens when the quantity of risk changes?. Understanding Risk: Roadmap. Defining Risk Measuring Risk The Risk-Return Tradeoff Sources of Risk Reducing Risk.
Risk is a measure of uncertainty about the future payoff of an investment, measured over some time horizon and relative to a benchmark.
Example: Single Coin Toss
Lists all possibilities, one of them must occur.
Probabilities sum to one.
Two possibilities are equally likely
Expected Value = ½ ($700) + ½ ($1400) = $1050
What if $1000 Investment
Expected Value = 0.1x($100) + 0.4x($700) + 0.4x($1400) +0.1x($2000) = $1050
A risk-free asset is
an investment whose future value is known with certainty
whose return is the risk-free rate of return.
1. Compute the expected value:
($1400 x ½) + ($700 x ½) = $1050.
2. Subtract this from each of the possible payoffs:
$1400 – $1050= $350
$700 – $1050= –$350
3. Square each of the results:
$3502= 122,500(dollars)2 and
4. Multiply each result times its probability and add up the results:
½ [122,500(dollars)2] + ½ [122,500(dollars)2] =122,500(dollars)2
5. Standard deviation = = =$350
Case 1: Standard Deviation =$350
Case 2: Standard Deviation =$528
The greater the standard deviation, the higher the risk.
Case 2 has a higher standard deviation because it has a bigger spread
The riskier an investment – the higher the compensation that investors require for holding it – the higher the risk premium.
More risk Bigger risk premium Higher expected returnRisk Requires Compensation
1. Idiosyncratic or Unique: Affects a specific a person or business.
2. Systematic or Economy-wide Risk:Affects everyone
Reduce overall risk by making two investments with opposing risks.
1. Invest $100 in GE
2. Invest $100 in Texaco
3. Invest ½ in each:
$50 in GE
+ $50 in Texaco
Hedging has eliminated the risk entirely.
Consider three investment strategies:
1. GE only,
2. Microsoft only, and
3. ½ in GE + ½ in Microsoft.
The more independent sources of risk in your portfolio, the lower the overall risk
End of Chapter