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Money & Banking ­ MGT411
VU
Lesson 11
MEASURING RISK
Measuring Risk
Variance and Standard Deviation
Value at Risk (VAR)
Risk Aversion & Risk Premium
Measuring Risk
Most of us have an intuitive sense for risk and its measurement;
The wider the range of outcomes the greater the risk
A financial instrument with no risk at all is a risk-free investment or a risk-free asset;
Its future value is known with certainty and
Its return is the risk-free rate of return
If the risk-free return is 5 percent, a $1000 risk-free investment will pay $1050, its expected
value, with certainty.
If there is a chance that the payoff will be either more or less than $1050, the investment is
risky.
We can measure risk by measuring the spread among an investment's possible outcomes. There
are two measures that can be used:
Variance and Standard Deviation
Measure of spread
Value at Risk (VAR)
Measure of riskiness of worst case
Variance
The variance is defined as the probability weighted average of the squared deviations of the
possible outcomes from their expected value
To calculate the variance of an investment, following steps are involved:
Compute expected value
Subtract expected value from each possible payoff
Square each result
Multiply by its probability
Add up the results
Compute the expected value:
($1400 x ) + ($700 x ) = $1050.
Subtract this from each of the possible payoffs:
$1400-$1050= $350
$700-$1050= ­$350
Square each of the results:
$3502  = 122,500(dollars)2 and
(­$350)2 = 122,500(dollars)2
Multiply each result times its probability and adds up the results:
[122,500(dollars)2] + [122,500(dollars)2]
= 122,500(dollars)2
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Money & Banking ­ MGT411
VU
More compactly;
Variance = ($1400-$1050)2 + ($700-$1050)2
= 122,500(dollars)2
Standard Deviation
The standard deviation is the square root of the variance, or:
Standard Deviation (case 1) =$350
Standard Deviation (case 2) =$528
The greater the standard deviation, the higher the risk
It more useful because it is measured in the same units as the payoffs (that is, dollars and not
squared dollars)
The standard deviation can then also be converted into a percentage of the initial investment,
providing a baseline against which we can measure the risk of alternative investments
Given a choice between two investments with the same expected payoff, most people would
choose the one with the lower standard deviation because it would have less risk
Value at Risk
Sometimes we are less concerned with the spread of possible outcomes than we are with the
value of the worst outcome.
To assess this sort of risk we use a concept called "value at risk."
Value at risk measures risk at the maximum potential loss
Risk Aversion
Most people don't like risk and will pay to avoid it; most of us are risk averse
A risk-averse investor will always prefer an investment with a certain return to one with the
same expected return, but any amount of uncertainty.
Buying insurance is paying someone to take our risks, so if someone wants us to take on risk we
must be paid to do so
Risk Premium
The riskier an investment ­ the higher the compensation that investors require for holding it ­
the higher the risk premium
Riskier investments must have higher expected returns
There is a trade-off between risk and expected return;
You can't get a high return without taking considerable risk.
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Money & Banking ­ MGT411
VU
Figure: The Trade-off between Risk and Expected Return
Higher Risk=Higher Expected Return
The higher the risk, the higher
the expected return. The risk
Risk Premium
premium equals the expected
return on the risky investment
minus the risk-free return.
Risk- Free Return
Risk
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Table of Contents:
  1. TEXT AND REFERENCE MATERIAL & FIVE PARTS OF THE FINANCIAL SYSTEM
  2. FIVE CORE PRINCIPLES OF MONEY AND BANKING:Time has Value
  3. MONEY & THE PAYMENT SYSTEM:Distinctions among Money, Wealth, and Income
  4. OTHER FORMS OF PAYMENTS:Electronic Funds Transfer, E-money
  5. FINANCIAL INTERMEDIARIES:Indirect Finance, Financial and Economic Development
  6. FINANCIAL INSTRUMENTS & FINANCIAL MARKETS:Primarily Stores of Value
  7. FINANCIAL INSTITUTIONS:The structure of the financial industry
  8. TIME VALUE OF MONEY:Future Value, Present Value
  9. APPLICATION OF PRESENT VALUE CONCEPTS:Compound Annual Rates
  10. BOND PRICING & RISK:Valuing the Principal Payment, Risk
  11. MEASURING RISK:Variance, Standard Deviation, Value at Risk, Risk Aversion
  12. EVALUATING RISK:Deciding if a risk is worth taking, Sources of Risk
  13. BONDS & BONDS PRICING:Zero-Coupon Bonds, Fixed Payment Loans
  14. YIELD TO MATURIRY:Current Yield, Holding Period Returns
  15. SHIFTS IN EQUILIBRIUM IN THE BOND MARKET & RISK
  16. BONDS & SOURCES OF BOND RISK:Inflation Risk, Bond Ratings
  17. TAX EFFECT & TERM STRUCTURE OF INTEREST RATE:Expectations Hypothesis
  18. THE LIQUIDITY PREMIUM THEORY:Essential Characteristics of Common Stock
  19. VALUING STOCKS:Fundamental Value and the Dividend-Discount Model
  20. RISK AND VALUE OF STOCKS:The Theory of Efficient Markets
  21. ROLE OF FINANCIAL INTERMEDIARIES:Pooling Savings
  22. ROLE OF FINANCIAL INTERMEDIARIES (CONTINUED):Providing Liquidity
  23. BANKING:The Balance Sheet of Commercial Banks, Assets: Uses of Funds
  24. BALANCE SHEET OF COMMERCIAL BANKS:Bank Capital and Profitability
  25. BANK RISK:Liquidity Risk, Credit Risk, Interest-Rate Risk
  26. INTEREST RATE RISK:Trading Risk, Other Risks, The Globalization of Banking
  27. NON- DEPOSITORY INSTITUTIONS:Insurance Companies, Securities Firms
  28. SECURITIES FIRMS (Continued):Finance Companies, Banking Crisis
  29. THE GOVERNMENT SAFETY NET:Supervision and Examination
  30. THE GOVERNMENT'S BANK:The Bankers' Bank, Low, Stable Inflation
  31. LOW, STABLE INFLATION:High, Stable Real Growth
  32. MEETING THE CHALLENGE: CREATING A SUCCESSFUL CENTRAL BANK
  33. THE MONETARY BASE:Changing the Size and Composition of the Balance Sheet
  34. DEPOSIT CREATION IN A SINGLE BANK:Types of Reserves
  35. MONEY MULTIPLIER:The Quantity of Money (M) Depends on
  36. TARGET FEDERAL FUNDS RATE AND OPEN MARKET OPERATION
  37. WHY DO WE CARE ABOUT MONETARY AGGREGATES?The Facts about Velocity
  38. THE FACTS ABOUT VELOCITY:Money Growth + Velocity Growth = Inflation + Real Growth
  39. THE PORTFOLIO DEMAND FOR MONEY:Output and Inflation in the Long Run
  40. MONEY GROWTH, INFLATION, AND AGGREGATE DEMAND
  41. DERIVING THE MONETARY POLICY REACTION CURVE
  42. THE AGGREGATE DEMAND CURVE:Shifting the Aggregate Demand Curve
  43. THE AGGREGATE SUPPLY CURVE:Inflation Shocks
  44. EQUILIBRIUM AND THE DETERMINATION OF OUTPUT AND INFLATION
  45. SHIFTS IN POTENTIAL OUTPUT AND REAL BUSINESS CYCLE THEORY