Transcript Chapter 11

Chapter 11: Hedging and
Insuring
Objective
Explain market mechanisms for
implementing hedges and insurance
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Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley
Chapter 11 Contents
11.1 Using Forward & Futures
Contracts to Hedge Risks
11.6 Basic Features of
Insurance Contracts
11.2 Hedging ForeignExchange Risk with Swap
Contracts
11.7 Financial Guarantees
11.3 Hedging Shortfall-Risk by
Matching Assets to
Liabilities
11.4 Minimizing the Cost of
Hedging
11.5 Insuring versus Hedging
11.8 Caps & Floors on Interest
Rates
11.9 Options as Insurance
11.10 The Diversification
Principle
11.11 Insuring a Diversified
Portfolio
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11.1 Using Forward and
Futures Contracts to Hedge
Risks
• Forward Contract
– an agreement between two parties to
exchange something at a specified price and
time
• This is an obligation on both parties
• Distinguish this from a right, but not the
obligation, of a party to exchange something
• To nullify the contract, you try to negotiate
second contract for a +/- cash consideration
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Definitions of Terms
• Forward Price
– Price (agreed to today) of an item to be
purchased, and paid for, at a given future date
• Spot Price
– Price (agreed to today) of an item to be
purchased (and paid for) immediately
• Face Value
– ‘Quantity of deliverable’ times ‘forward price’
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Definitions of Terms
• Long Position
– The agreement to buy the item (from the
person taking the short position)
• Short Position
– The agreement to sell the item (to the
person taking the long position)
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Using Forward and Futures
Contracts to Hedge Risks
• Traditionally, no payment is made on a
forward contract until the settlement date
– If the parties to a forward contract do not
trust the other, then add clauses to
• provide a sureties to a stakeholder
• periodically render contract valueless by
making cash settlement equal to its current
market value
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Using Forward and Futures
Contracts to Hedge Risks:
Futures Contracts
• Futures contracts for commodities and
financial products includes such clauses
to protect against unknown credit risks,
and we leave the details of this to
Chapter 14
• For clarity, the following example treats
futures as if they were pure forward
contracts
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The Farmer and the Baker
(Example)
• Jamela is a farmer with a wheat crop of
about 100,000 bushels, 1-month from
harvest
• Mohammed is a baker who will need to
restock his inventory of wheat for the
coming year
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The Farmer and the Baker
• Jamela and Mohammed wish to reduce
price uncertainty because:
– Jamela has a mortgage to pay on her farm,
and is concerned about wheat prices falling
in the next month
– Mohammed wishes to close an agreement
with a supermarket to supply bread at a
fixed price for the coming year
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The Farmer and the Baker
• Jamela and Mohammed agree to a
forward contract
– Jamela agrees to deliver 100,000 bushels of
wheat at $2.00 a bushel in one month, and
Mohammed agrees to pay the $200,000 on
delivery
– Assuming the crop doesn't fail, both parties
have hedged their obligations
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The Farmer and the Baker
• Assume that Jamela and Mohammed live
miles apart, and don’t know each other
• Jamela writes a forward contract with Ms.
Distributor at $1.99/bushel
• Mohammed writes a forward contracts with
Mr. Supplier at $2.01/bushel
• Ms. Distributor, Mr. Supplier, and Dr. Another
hedge with forward contracts at $2.00/bushel
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The Farmer and the Baker
• Move forward a month
– Wheat prices are not $2.00 a bushel, but
$2.20, due to wet conditions in other
geographic regions
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The Farmer and the Baker
– Jamela’s crop is 110,000 bushels, and it also
exceeds the contracted quality
– She delivers the contracted 100,000b for the
agreed $2.00/bushel, and receives $200,000
– She sells her surplus 10,000b at $2.20 +
$0.10 (a quality premium) to a local baker,
and receives $23,000
– The total = $223,000
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The Farmer and the Baker:
Alternative Strategy
– Jamela buys 100,000 Bushels of deliverable
quality wheat @ $2.2/b for -$220,000,
delivers it to Ms. Distributor, and receives the
agreed $200,000. Loss of $20,000
– She sells her 110,000b at $2.20 + $0.10
quality premium to a local baker and
receives $253,000
– The total = $233,000 ($10,000 more)
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The Farmer and the Baker:
Alternative Strategy
• The product to be delivered was to meet
or exceed a certain quality
• Jamela would have been foolish to
deliver her wheat when a lower quality
wheat was available for delivery at a
lower price
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The Farmer and the Baker:
Alternative Strategy
• Mohammed bakes a premium bread
• He too could devise a strategy to reduce
risk using the forward contract, but also
receive premium quality wheat
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The Farmer and the Baker:
Next Development
• The forward contracts always specify the
minimum deliverable quality, and often a
formula for delivering other qualities
• A market in forward contracts may be
devised that encourages cash settlement,
and discourages physical delivery
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The Farmer and the Baker:
Next Development
– Jamela sells forward 200,000b for 1-month
delivery @ 2.00 / bushel
• This short has no monetary value at this time
– A month later, the spot price of deliverable
wheat is $2.20 / b, and the forward is about
to expire, and so is also trading at $2.20 / b
– The contract now has a monetary value.
The long position is worth $(2.20 - 2.00) /
bushel
• Jamela settles her position by paying $20,000
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The Farmer and the Baker:
Next Development
– Jamela has made a loss of $20,000 on her
trade in the hypothetical wheat forwards
market
– She recovers this loss when she sells her
wheat
• This is a true hedge. She has lost the
opportunity to participate in a rise in the price
of wheat in return for down-side protection
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The Farmer and the Baker:
Next Development
– The baker’s hedge in the forward market
resulted in a settlement of $20,000
– When he takes physical delivery, he exactly
offsets higher spot prices with this $20,000
– He traded the opportunity of lower wheat
prices for a known price
• Both gained! Mohammed’s gain (at Jamela
expense) is 20/20 hindsight, and should be
irrelevant to both of them
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The Farmer and the Baker:
Next Development
• Omar is rich, and wants to get richer
– He purchases forward 100,000b of wheat @
$2.00/bushel, for delivery in 1-month
– At maturity, deliverable wheat costs $2.20/b
and he makes a cash settlement, gaining
$20,000
– Omar is a speculator profiting from his
purported understanding of the market
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The Farmer and the Baker:
Next Development
• Rema wants to get rich too
– She sells forward 100,000b of wheat @
$2.00/bushel for delivery in 1-month
– At maturity, deliverable wheat costs $2.20/b
but she is unable pay the $20,000 she owes
– Rema’s default must be made good by one
or more of the market’s participants
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The Farmer and the Baker:
Forwards to Futures
• To mitigate default-risk exposure
– Require a modest surety deposit based on
daily volatility
– Mark contract to market daily (rendering
them temporally valueless)
• The small profit/loss is payable immediately
– Remaining problem: Large daily price
movements
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The Farmer and the Baker:
Conclusion
• The farmer and the baker have both
eliminated specific risks through perfectly
anti-correlated assets
• Speculators are exposed to considerable
risk, hoping to enjoy a statistical profit
– They provide liquidity and expertise that
push the market further towards efficiency
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Risk Transfer: Three Points
• Whether the transaction reduces or increases risk
depends upon the particular context in which it is
undertaken
• Both parties to a risk-reducing transaction can benefit.
In retrospect, it may seem as if one of the parties has
gained at the expense of the other
• Even with no change in total output nor total risk,
redistributing the way the risk is borne can improve the
welfare of the individuals involved
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11.2 Hedging ForeignExchange Risk with Swap
Contracts
• Swap Contract
– an agreement between two parties to
exchange a series of cash flows, at specific
intervals, over a specified period of time
– the swap payments are based on an agreed
principal amount (the notional amount)
– there is no immediate payment of money to
either party as compensation for entering
the contract
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Hedging Foreign-Exchange
Risk with Swap Contracts
• A swap may call for the exchange of
anything, but most swaps are for the
exchange of
– commodities
– currencies
– securities’ returns
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Currency Swap Example
• You have an agreement with a German
software distributor for them to market
the German language version of your
financial derivative pricing program for a
payment of DM100,000/year for 10 years
• To hedge foreign exchange risk,
immunize your future DM to $US
transactions using a currency swap
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agreement
Currency Swap Example
• This swap arrangement is equivalent to a
series of forward foreign exchange
contracts
• The notional amount in the swap
contract corresponds to the face value of
the implied forward contracts
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Currency Swap Example
• You are still at risk after the swap
– Default: There is a probability that the
German company will default on its
agreement, either by going bankrupt, or by
exercising a performance clause in the
contract
– Default driven Exchange Risk: Should
default occur, you reacquire exchange risk
through the residual swap agreement
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Currency Swap Example
• Suppose the spot exchange rate is
$0.50/DM
• You and the counterparty agree that the
forward exchange rates should decline
from the current spot by 2% per year
(rounded) for 5 years, and then remain
static
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Currency Swap Example
• The forward rates are then agreed to be:
0.49, 0.48, 0.47, 0.46, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45
• Assume the actual spot rates are:
0.50, 0.51, 0.53, 0.51, 0.49, 0.48, 0.48, 0.47, 0.45, 0.43
• The flows from/ to the counterparty are
computed as (Forward - Spot)*notional
amount
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Currency Swap Example
• (0.49-0.50)*100,000 DM = $1,000 (Year 1)
• (0.48-0.51)*100,000 DM = $3,000 (Year 2)
• (0.47-0.53)*100,000 DM = $6,000 (Year 3)
• (0.46-0.51)*100,000 DM = $5,000 (Year 4)
• (0.45-0.49)*100,000 DM = $4,000 (Year 5)
• (0.45-0.48)*100,000 DM = $3,000 (Year 6)
• (0.45-0.48)*100,000 DM = $3,000 (Year 7)
• (0.45-0.47)*100,000 DM = $2,000 (Year 8)
• (0.45-0.45)*100,000 DM = $0,000 (Year 9)
• (0.45-0.43)*100,000 DM = $2,000 (Year 10)
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Currency Swap Example
• In the first year, the agreed forward rate
is lower than the actual spot, resulting in
a flow from your USA-based company to
the counter-party of $1,000
• The sale of DM yields
• 100,000DM*0.50$/DM = $50,000
• After payment to counterparty = $49,000
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Currency Swap Example
• Whatever the spot rate in year 1, the
agreement absorbs the variance, and you
receive a net $49,000 (guaranteed)
• Assuming no default, the guaranteed net
cash flows ($ ’000) are
• Year 1 = 49, year 2 = 48, year 3 = 47,
year 4 = 46, year 5 through year 10 = 45
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Currency Swap Example
– If you prefer a dollar annuity, negotiate:
• a fixed forward rate with the counterparty
Assume a single forward rate (rather than a schedule based
on market expectations formed from the $ & DM yield
curves). With the passage of time, the expected market
value of the swap will diverge more from zero. This
generates higher credit risk for the counterparty, which
translates into higher costs for you
a new DM payment schedule that, when
coupled with the swap, generates a constant
$ payment schedule
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11.3 Hedging Shortfall-Risk
by Matching Assets to
Liabilities
• Assume a credit union borrows using 1year CDs, and lends using 30-year
mortgages
– If interest rates rise
• the market value of the mortgages will fall
• mortgage cash flows won’t fully pay the CDs
– Result? Insolvency and ruin!
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Value of 30-Year Mortgage 5-Years Out (6%)
16,000,000
Market Value of Mortgages
Market Value of Mortgage
14,000,000
12,000,000
10,000,000
8,000,000
6,000,000
4,000,000
Book Value of Mortgages
2,000,000
0
1%
3%
5%
7%
Market Interest Rate
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9%
11%
Interpretation
– Five years later, interest rates will have risen
or fallen
• The more rates have risen above the
mortgages’ coupon rate, the larger the
unrealized capital loss, but liabilities remain
essentially constant
• The more rates have fallen below the
mortgages’ coupon rate, the higher the
unrealized capital gain, but the more likely
borrowers will refinance. (Graph assumes no
refinancing)
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Cash from Mortgages and Cash Needed for CDs
Cash Flows From Mortgages and to
CDs
1,200,000
CD Interest Payments
1,000,000
800,000
600,000
400,000
Mortgage Interest Payments
200,000
0
1%
2%
3%
4%
5%
6%
7%
8%
Current Interest Rate
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9% 10% 11% 12%
Interpretation
• As interest rates rise, so too does the
rate demanded by the lenders
• The mortgage borrowers continue to
provide the same cash flow
• The result is a reduction in the cash flows
that service the CDs
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Remedial Action to Prevent
further Damage
– Match exposure of assets and liabilities
• Sell mortgages & invest in short-term lending
– Participate in GNMA, FNMA, … programs
• Get lenders to invest in longer-term notes
• Lend using adjustable rate mortgages
• Issue longer-term bonds
– Hedge using interest-rate forwards, futures,
options, or swaps
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11.4 Minimizing the Cost of
Hedging
• There are sometimes several ways to
hedge a transaction
– Choose the one that minimizes the cost of
achieving the desired level of risk reduction
after considering transaction costs, and taxes
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11.5 Hedging versus Insuring
– Hedging: A contract “to purchase 100,000
perfume bottles, six months from now @
$0.25/bottle, payment on receipt” is a
forward contract (obligation to purchase)
– Insuring: A contract “to purchase up to
100,000 perfume bottles, six months from
now @ $0.25/bottle, payment on receipt” is
a not a forward contract (right but no
obligation to purchase)
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Hedging versus Insuring
• Recall
– Hedging is symmetric, you sacrifice the
upside risk to protect you against the
downside risk
– Insuring is asymmetric, you maintain the
upside risk, but dispose of the downside risk
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Hedging v. Insuring
450000
400000
Revenue from Wheat
350000
Hedged
Insured
300000
250000
200000
150000
100000
50000
0
0
0.5
1
1.5
2
2.5
Price of Wheat
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3
3.5
4
11.6 Basic Features of
Insurance Contracts
• Exclusions
• Caps
• Deductibles
• Co-payments
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11.7 Financial Guarantees
• Financial guarantees are insurance
against credit risk--the risk to you that
the counterparty will default
• A loan guarantee is a contract that
obliges the guarantor to make the
promised payment on a loan if the
borrower fails to do so
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11.8 Caps and Floors on
Interest Rates
• Some financial instruments, such as
ARMs, offer an interest rate that varies
with a specified prime rate, the T-bill
rate, LIBOR, et cetera
• A clause may provide for annual floors,
annual caps, global floors, or global caps
on interest rate changes
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11.9 Options as Insurance
• A call (put) option is the right, but not
the obligation, to purchase (sell) a given
asset according to a schedule of prices
and times
• European options have a single strike or
exercise price, and a single exercise date
• American options have a single strike or
exercise price, and may be exercised at any
time before their expiration
or maturity date
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Options as Insurance: Put
Illustration
• You have 100 shares of XYZ stock
currently trading at $100/share, and a
planning time horizon of 3-months
• You wish to pay a small premium to
insure the current price in 3-months
• You wish to benefit from any stock price
rises
51
Options as Insurance: Put
Illustration
• Strategy:
– Retain your holding of 100 shares in XYZ
currently valued at $10,000
– Purchase one round lot of 100 XYZ European
put options with a strike price of $100 for a
premium of $729.51
– At the end of 3-months, your holding, as a
function of XYZ new share price, is:
52
Hedging with a Put
16000
14000
12000
10000
Share Holding
Value Puts
FV Premium
Total Wealth
8000
6000
4000
2000
0
50
60
70
80
90
100
110
-2000
Share Price
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120
130
140
150
Put Option on a Bond
• The value of a bond depends upon
– the risk-free rate for bonds of that maturity
– the value of the bond’s collateral
• Purchasing a put option on the bond
gives downside protection, while
preserving upside potential
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11.10 The Diversification
Principle
• Diversification:
– splitting an investment among many risky
assets instead of concentrating it all in only
one
• Diversification Principle:
– by diversifying across risky assets people can
sometimes achieve a reduction in their
overall risk exposure with no reduction in
their return
55
Diversification of Uncorrected
Risks
• Assume that you are offered a number of
investment opportunities in various
biotechnology firms
– The outcome of any of the investments has
no effect on any of the others (independent)
– You believe that each firm has a 50% chance
of quadrupling your investment, and a 50%
chance of total loss
56
Invest $100,000 in any one of
the firms:
– If the firm fails (p = 0.50)
• the expected contribution to your pay-out is
0.50 * $0 = $0
– If the firm is successful (p = 0.50)
• the expected contribution to your pay-out is
0.5 * 4 * $100,000 = $200,000
– Expected Pay-off = $0 + $200,000 =
$200,000
57
Invest $50,000 in any of the
firms, & $50,000 in another
– If both firm fails (p = 0.25)
• the expected contribution to your pay-out is 0.25 * $0
= $0
– If one firm is successful (p = 0.50)
• the expected contribution to your pay-out is 0.5 * 4 *
$50,000 = $100,000
– If both firm are successful (p = 0.25)
• the expected contribution to your pay-out is 0.25 * 4 *
2 * $50,000 = $100,000
– Expected Pay-off = $0 + $100,000 + 100,000 = $200,000
58
Conclusion
• Investing in one or in two firms has the
same expected return
• But...
59
But...
• We have not analyzed risk
– We will now compute the standard
deviations of both strategies
60
Standard deviation, 1 firm
State of the World Probability
One Failure
One Success
0.5
0.5
Payoff
0
400000
Mean
200000
200000
Deviation
Dev SQR
-200000
200000
4E+10
4E+10
<- * Prob
2E+10
2E+10
Sum =
4E+10
Sqrt ^|
200000
•The Standard Deviation is $200,000
61
Standard deviation, 2 firms
State of the World Probability
One Failure
One Success
Two Successes
0.25
0.5
0.25
Payoff
0
200000
400000
Mean
Deviation
200000
200000
200000
Dev SQR
-200000
0
200000
4E+10
0
4E+10
<- * Prob
1E+10
0
1E+10
Sum =
2E+10
Sqrt ^|
141421.356
•The Standard Deviation is
about $141,000 (c.f. $200,000)
62
Standard deviation, equal
investment in “n” firms
• Generalizing the argument, it is easy to
prove that the standard deviation in this
case is just $200,000/SqrareRoot(n)
• Conclusion: Given the facts of this
example, the risk may be made as close
to zero as we wish if there are sufficient
securities! In reality, however …
n is must be finite, and pharmaceutical projects have a non-zero correlations
63
Correlated Homogeneous
Securities
• Pharmaceutical projects do have positive
correlation (Why?)
• Loosen the assumptions made about the
correlation, and set it to ρ, and use the
generalization of
  w   w   2w1w21 2 1,2
2
p
2 2
1 1
2
2
2
2
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Correlated Homogeneous
Securities
• We obtain the relationship
σport= σsec *QSRT(ρ + 1/n)
• In the case of n -> Infinity, there remains
the term
σport= σsec *QSRT(ρ)
• This risk is not diversifiable
65
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.2, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
Portfolio Size
66
35
40
45
50
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.8, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
Portfolio Size
67
35
40
45
50
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.5, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
Portfolio Size
68
35
40
45
50
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.2, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Diversifiable Security Risk
Nondiversifiable Security Risk
0
5
10
15
20
25
30
Portfolio Size
69
35
40
45
50
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.0, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
All risk is diversifiable
0
5
10
15
20
25
30
Portfolio Size
70
35
40
45
50
Negative Correlation
• Note that as the correlation ranges from
one to zero
– the percentage of undiversifiable risk falls
– the number of securities necessary to
approach this level increases
• …and just for fun, let’s look at a negative
correlation
71
Standare Deviation
Standard Deviations of Portfolios,
rho = 1/(1-50) = -0.0204, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
Portfolio Size
72
35
40
45
50
Nondiversifiable Risk
• The graphs illustrate an important point
– For homogeneous securities (at least), there
is an asymptotic value for the least risk a
portfolio may contain
– For correlations that are strictly positive,
there appears to be a level of risk that can’t
be diversified away
73
Nondiversifiable Risk
• For a fund manager, the cost of holding
her assets in either (1) a well diversified
portfolio, or (2) a single stock, differ by
only (quite low) transaction costs
• In this world of homogeneous securities,
she may reduce risk by diversifying some
of the risk away at (almost) no cost
74
Language
• The following groups of word are similes
– Diversifiable risk, individual risk, securityspecific risk, irrelevant risk
– Nondiversifiable risk, market risk, relevant
risk
75
11.11 Diversification & the
Cost of Insurance
• When you purchase insurance, the
premium, p, may be divided into two
portions
– a, the actuary value of the good-faith risk
– b, the sales, administration, profits, and
fraud
• The ratio a/p not always as high as one
would like
76
Self-Insurance
• Accordingly, accepting some of the risk
yourself may be advisable in some
situations
– When the correlation between risks is not
high
– when the number of risks is relatively high
– when the risks are of the same magnitude
77