CHAPTER 5Understanding Risk

Understanding Risk

Defining Risk

Risk is a measure of uncertainty about the possible future pay offs of an investment. It is measured over some time horizon, relative to a benchmark.

Risk is a measure that can be quantified. Uncertainties that are not quantifiable cannot be priced.

Understanding Risk Risk arises from uncertainty about the future.

Risk has to do with the future payoff of an investment, which is unknown. Imagining all the possible payoffs and the likelihood of each one is a difficult but indispensable part of computing risk.

The definition of risk refers to an investment or group of investments. Risk must be measured over some time horizon. In most cases the risk of holding an investment over a short period of time is smaller than holding it over a long one.

Risk must be measured relative to a benchmark rather than in isolation.

Understanding Risk

Measuring RiskMeasuring risk is crucial to understanding the financial system.

Possibilities, Probabilities, and Expected Value To study random future events, start by listing all the possibilities and assign a probability to each. Be sure the probabilities add to one.

Probability is a measure of the likelihood that an event will occur. Its always expressed as a number between zero and one.

Understanding RiskA simple example: All possible Outcomes of a single Coin Toss

In constructing a table like this one, we must be careful to list all possible outcomes. One important property of probabilities is that one or the other event will happen. If the table is constructed correctly, then, the values in the probabilities column will sum to one

Understanding Risk

The expected value is the probability-weighted sum of all possible future outcomes.

Understanding Risk

Measures of Risk

A risk-free asset is an investment whose future value, or payoff, is known with certainty.

Risk increases when the spread (or range) of possible outcomes widens but the expected value stays the same.

Understanding Risk

Variance and standard Deviation: One measure of risk is the standard deviation of the possible payoffs. It takes several steps to compute the variance of an investment.-Compute the expected value: 1/2 ($1,400)+1/2 ($700) = $1,050 -Subtract the expected value from each of the possible payoffs: $1,400 - $1,050 = +$350 $700 - $1,050 = -$350 -Square each of the results: $350 = 122,500(dollars)2 and (-$350) 2 = 122,500(dollars) 2 -Multiply each result times its probability and add up the results: 1/2[122,500(dollars) 2 ]+ [122,500(dollars) 2 ]2

Understanding Risk

Writing this procedure more compactly, we getVariance = ($1,400 - $1,050) 2 + ($700 - $1,050) = 122,500(dollars) 2

The Standard deviation is the (positive) square root of the variance or:Standard deviation = Variance = 122,500 dollars2 = $350

Understanding Risk

Value at Risk A second measure of risk is value at risk, the worst possible loss over a specific time horizon, at a given probability.

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Understanding Risk

Risk Aversion, the Risk Premium, and the Risk-Return Trade-off

A Risk Averse Investor Always prefers a certain return to an uncertain one with the same expected return.

Requires compensation in the form of a risk premium in order to take risk.

Trades off between risk and expected return: the higher the expected return risk-averse investors will require for holding an investment.

Understanding Risk

The trade-off between Risk and Expected Return

Understanding Risk

Sources Of Risk Idiosyncratic Risk: its specific to a particular business or circumstance.

Systematic Risk: its common to everyone

Understanding Risk

Reducing Risk through Diversification

There are two types of diversification: Hedging: in which investors reduce idiosyncratic risk by making investments with offsetting payoff patterns. Spreading: in which investors reduce idiosyncratic risk by making investments with independent payoff patterns.