Download Chapter 10 An Overview of Risk Management

Chapter 10
Financial Economics, Spring 2011
Chapter 10 An Overview of Risk Management
ü 10.1 What is Risk?
ü Is uncertainty the same as Risk ?
Uncertainty exists whenever one does not know for sure what will occur in the future. Risk is uncertainty that
"matters" because it affects people's welfare. Every risky situation is uncertain but there can be uncertainty
without risk.
Risk Aversion: This is a characteristic of an individual's preferences in risk-taking situations. It is a measure of
willingness to pay to reduce one's exposure to risk.
Example 1: You buy travel insurance to mitigate or eliminate risk of large unexpected payments. If you are more
risk averse, then you would pay more for larger insurance coverage.
Example 2: If you are willing to accept a lower expected rate of return on an investment because it offers a more
predictable rate of return, then you are risk averse.
ü Risk Management
Risk Management
The appropriateness of a risk-management decision should be judged in the light of the information available at
the time the decision is made. (quick-check 10-1)
Risk Exposure
If you face a particular type of risk because of your job, the nature of your business, or your pattern of consumption, you are said to have a particular risk exposure.
The riskiness of an asset or a transaction cannot be assessed in isolation or in the abstract. Is life insurance on
unrelated person risk reducing?
Speculator: Investors who take positions that increase their exposure to certain risks in the hope of increasing
their wealth.
Hedgers: Those who take positions to reduce their risk exposures.
ü 10.3 Risk-Management Process
Risk management process is a systematic attempt to analyze and deal with risk.
The risk-management process can be broken down into five steps:
1. risk identification
2. risk assessment; quantification of the costs associated with the risks that
have been identified. Related words;actuary, actuarial mathematics
3. Selection of risk-management techniques
4. implementation
5. review
Selection of Risk-management Techniques
risk avoidance; not entering certain business
loss prevention and control; reducing likelihood or the severity of loss
risk retention; absorbing the risk and preparing to cover losses out of one's own resources
risk transfer; buying insurance, for example.
ü 10.4 The Three Dimensions of Risk Transfer
You can transfer risk by hedging, insuring and diversifying.
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Chapter 10
Financial Economics, Spring 2011
1.Hedge: One is said to hedge a risk when the action taken to reduce one's exposure to a loss also causes one to
give up of the possibility of a gain.
2. Insuring: Insuring means paying a premium to avoid losses.
When you hedge, you eliminate the risk of loss by giving up the potential for gain. When you insure, you pay a
premium to eliminate the risk of loss and retain the potential for gain.
3. Diversifying: Diversifying means holding similar amounts of many risky assets instead of concentrating all of
your investment in only one.
Risk Management Example 1: Japanese exporter.
Company A will receive 1million dollars one month later. How to manage risk?
risk identification and assessment: It is exposed to fluctuations of foreign exchange rate. What are effects of
appreciation and depreciation of USD against JPY? How is it volatile?
choosing technique:
risk avoidance; have the export contract paid in JPY.
This is too late.
loss prevention and control; borrowing USD due one month. Exchanging
USD into JPY today and repay this borrowing by the proceeds of the
export contract.
risk retention; possible. Exchanging USD into JPY one month later.
risk transfer:
Selling USD at forward rate (hedging).
Or buying an option
contract of USD-put JPY- call (insuring).
Having export contracts in Euro
and other currencies(diversifying), but may be too late.
ü 10.4 The Three Dimensions of Risk Transfer
ü Risk Management Example: Japanese Exporter
Company A will receive 1million dollars one month later. How to manage risk?
(1) risk identification: The company is exposed to fluctuations of foreign exchange rate.
(2) assessment: What are effects of appreciation and depreciation of USD against JPY on the company's profit?
The company must quantify the effects of exchange rate change on its profit. And also the company must understand likeliness of these situation, i.e., probabilities.
(3) choosing technique
• risk avoidance; to have the export contract paid in JPY.
It is too late to implement this technique.
• loss prevention and control; borrowing USD due one month. Exchanging
USD into JPY today and repay this borrowing by the proceeds of the
export contract.
• risk retention; possible. Exchanging USD into JPY one month later.
• risk transfer:
1. hedging: Selling USD at forward rate.
2. insuring: buying an option; USD-put JPY- call .
3. diversifying: Having export contracts in Euro
and other currencies. But this technique cannot be implemented. It is too late.
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Chapter 10
Financial Economics, Spring 2011
ü 10.7 Portfolio Theory
Portfolio theory consists of formulating and evaluating the trade-offs between the benefits and cost of risk reduction in order to find an optimal course of action.The risk is measured by the standard deviation.
ü 10.8 Probability Distributions of Returns
Total rate of return from assets consists of two components; income component and price-change component. In
other wards, they are income gain and capital gain. In case of stocks, dividend is income gain. So the rate of return
is given by the following;
total rate of return =
cash dividend
begining price

ending price of a share beginning price
beginning price
These gains and accordingly, rate of returns are not certain most of the time. They are stochastic, i.e., random. We
consider bond price, stock price and their rate of returns random variables. With regard to random variable, we
want to know its on-average value and degree of dispersion of the value. To understand these values, we define
expected value and variance. Square root of variance is called standard deviation. Standard deviation is an
important parameter to determine option premiums. Also it plays an important role in the portfolio risk management.
ü Definition: Expected Value and Standard Deviation
Suppose random variable X takes values x1 ,... , xn with probability p1 ,... , pn . We denote expected value and
variance by E[X] and Var[X]. Rule of notation: Capital letter for random variable and small letter with subscript
for its specific values.
E[ X ] = nk1 pk xk
Var[ X ] = nk1 pk xk  EX2
Standard deviation is square root of variance.
ü Example: Table 10.1 on p284
ClearA, r, p, ER, VR
"state of
"rate of
"probability"
economy"
return"
A
"strong"
"normal"
"weak"
0.3
0.1
 0.1
;
0.2
0.6
0.2
Here we substitute values in the table A into variables r and p.
Table rk  A1  k, 2, k, 1, 3, 1
Table pk  A1  k, 3, k, 1, 3, 1
0.3, 0.1,  0.1
0.2, 0.6, 0.2
ü Expected value
ER   pk rk ; Print"ER  ", ER 
3
k1
ER  0.1
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Chapter 10
Financial Economics, Spring 2011
ü Variance and Standard Deviation
ER   pk rk ; VR   pk rk  ER2 ;
3
3
k1
Sd 
k1
VR ; Print"VarR  ", VR, "; S.D. ", Sd
VarR  0.016; S.D. 0.126491
ü Estimating expected value and variance
Often you do not know probability distribution. You have to estimate these. In many cases, it is assumed that
random Variables follows normal distribution. And you have to estimate expected value and variance to apply.
Usual method, which is called unbiased estimator, is as follows:
estimated expected value = average of samples = n ni1 xi
1
To estimate variance, if sample size is n, then denominator is n-1, instead of n:
1
n1
ni1 xi  x 2
ü Example: How much 1,000 yen bill should be put in ATM?
A bank manager wonders how many 1,000 yen bill he should put in the ATM at 9:00 am. The bank likes to avoid
a situation such that 1,000 yen bill runs out of machines and that customers go to another banks. He monitored
how much 1,000 yen bills have been deposited and withdrawn in one week. He wants to find expected value and
variance of the net amount of 1,000 yen bill deposited and withdrawn. On Saturday and Sunday, these ATM are
closed.
ClearA, k
A
"day"
"net amount of
1,000 yen bill"
"Monday"
"Tuesday"
"Wednsday"
"Thursday"
"Friday"
1890
2901
1703
 205
 1020
;
Clearn, average, samplevariance, sd; n  5; average  N
1
n
samplevariance  N
1
n 1
 A1  k, 2  average2 
n
k1
1053.8
2.60452  106
sd 
samplevariance
1613.85
ü Application
InverseCDFNormalDistributionaverage, sd, 0.001
 3933.38
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 A1  k, 2
n
k1
Chapter 10
Financial Economics, Spring 2011
If he put 3,934 of 1,000 bill in ATM, then probability that ATM runs out 1,000 yen bill will be less than 0.1%.
ü Homework No.5 due on May 25, 2010
Q1. p.293 10.19, Q2 10.20, Q3 10.21, Q4 p.294 10.22
ü About Mathematica: making table or matrix
ü Making a table in input mode
• If you use a table, it is easier to organize parameter values. Choose “input”- table( M) - new ( N ). You can
choose number of rows and columns. You can identify an element of a table or matrix by A [[ row number ,
column number ] ] .
• Mathematica reads all the entries in the table in “input mode”. If you want to use letters as words, not as
variable name, wrap them with quotation marks as in the example.
• Copy and paste in the text mode, if you like to use the table between your sentences.
ü Array variable
The same variable name with different ID numbers can be specified by “variable name[ ID number ] “, like p[k]
and r[k] in the above example. Use of array variable save your time to substitute values into variables.
ClearA, k
A
"day"
"net amount of
1,000 yen bill"
"Monday"
"Tuesday"
"Wednsday"
"Thursday"
"Friday"
1890
2901
1703
 205
 1020
;
The table is denoted by “A”. Value 18 at the 2nd row and 2nd column is specified as A[ [ 2, 2 ] ] ;
Name of table [[ row ID , column ID ]].
A2, 2
1890
A[ [ 1+k, 2 ] ] means (1+k) th row and 2nd column in the table. Why 1+k ? The 1st row is for labels of the data.
A
Clearn, average, samplevariance, sd; n  5;
average  N
1
n
sd 
 A1  k, 2; samplevariance  N
n
1
k1
n 1
 A1  k, 2  average2 ;
n
k1
samplevariance ;
He assumes that net amount of 1,000 bill follows normal distribution. He want to know how many 1,000 yen bill
he should put in the morning so that probability of running out of 1,000 yen bill is less than 0.1%. This means to
find value of x such that Probability( X< x ) = 0.001 where X follows normal distribution.
InverseCDFNormalDistributionaverage, sd, 0.001
 3933.38
Probability such that net amount 3,934 of 1,000 yen bill is withdrawn is less than 0.1%.
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