Chapter 6 - pt 1 Lecture Notes - 8-07 - Risk and Risk Aversion BKM Chapter 6 part 1 What is risk How do we measure risk The trade-off between risk and

# Chapter 6 - pt 1 Lecture Notes - 8-07 - Risk and Risk...

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Risk and Risk Aversion BKM Chapter 6 – part 1 What is risk? How do we measure risk? The trade-off between risk and return Risk-return assumptions of portfolio theory Utility functions and indifference curves
Risk Q) What is risk? A) Two definitions, both correct : Risk means more things can happen than will happen - Elroy Dimson, a famous finance professor My momma always said, “Life is like a box of chocolates. You never know what you’ll get next.” - Forrest Gump Risk and Return: The trade-off Consider the following choice facing an investor with \$100,000 to invest. She has the choice of investing the \$100,000 in a risk-free investment or a risky investment. Possible payoffs of both investments are: Risk-free investment 100,000 105,000 Risky investment 150,000 100,000 80,000 The (simple) return on the risk-free investment is: 105,000 1 100,000 f r = - = 5% 2
The expected return on the risky investment is: 150,000 80,000 ( ) 0.6 1 0.4 1 22% 100,000 100,000 50% 20% E r = - + - = - % 1 442 4 43 1 442 4 43 Which investment should our investor choose? To try and make a decision, we proceed in three steps: Step 1 : Calculate the risk premium or expected excess return on the risky investment. Definition : The risk premium on any risky asset is its expected return over and above the risk-free rate: ( ) ( ) ( ) e f f E r E r r E r r = - = - % % % - For our risky investment, ( ) ( ) 0.6(50% 5%) 0.4( 20% 5%) ( ) = 22%-5% =17% e f f E r E r r E r r = - = - + - - = - % % % Step 2 : Calculate the risk of the risky investment. It is traditional to use variance or standard deviation of an investment’s return as a measure of its risk. - The variance of the risk-free investment is zero - The variance of the risky investment is: 2 2 2 ( ) 0.6 (0.50 0.22) 0.4 ( 0.20 0.22) r σ = - + - - = % 0.1176 and, the standard deviation is ( ) 0.1176 34.29% r σ = = % Step 3 : We need to decide whether the 17% risk premium is commensurate with the 34.29% risk. i.e. we need a way of telling us whether 17% is adequate compensation for this risk, more than adequate or less than adequate. 3
- This is NOT an easy question to answer; the whole field of asset pricing has developed (and continues to expand) to answer this one question. Asset Pricing Models like the CAPM and the APT are attempts to answer this question. - Before we jump into asset pricing models, we need to learn portfolio theory, and the first piece of this theory has to do with investors’ attitudes towards risk. i.e. we need to make some assumptions regarding investors.