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FINANCE
Review of Questions and Problems
Part IV: Chapter 10-12
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Three analytical “pillars” to finance:
 Optimization over Time（intertemporal trade-offs）:
Part II
 Asset Valuation（Principals of Asset Valuation &
Valuation of Bond and Stock）: Part III
 Risk Management—Part IV & V：Hedging
(Future/Forward), Insuring (Option/Equity Value ) ,
Diversifying (Portfolio Theory/CAPM )
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Chapter 10: A Overview of Risk
Management
Main
Contents:
The concepts of uncertainty and risk
The process of risk management
The concepts and discrimination of hedging, insuring,
diversifying
Risk transfer and its contributions to economic efficiency
Problems of homework: to understand accurately the
meanings of questions and to choose properly the
instruments for hedging and insuring
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Solutions:
A zero coupon bond is riskless or risk-free only in
term of certain unit of account and only if held
to maturity
10.3 – Treasury Bill is a common risk-free
(default-free) investment instrument
a. 3-months T-Bill
b. (zero coupon)20-years T-Bill
c. There are many risk-free investment
instruments depending upon circumstances.
Investment time horizon is critical to choosing
the best risk-free investment instrument
(matching in-payments with out-payments so that
you are left with no risk)
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10.6 –Inflation is a key risk factor
 a. The inflation-indexed T-Bill offers a fixed real rate
of return of 3% over the life of the investment. The real
return on the conventional T-Bill’s real return depends
upon the expected rate of inflation over the life of the
investment. The safer investment is the Inflation Plus
T-Bill
 b. The answer depends upon the expected rate of
inflation over the life of the investment
c. The real return on the index-linked T-Bill is 3%
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10.7 –To answer question b & c given your choice
in question a
a. Choose the 30-year fixed rate at 9%
b. The instrument in question a is the hedging, but not
insuring
c. Risk management costs = the opportunity cost = at
least 4% since I could get a variable rate loan at 5%
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Chapter 11: Hedging, Insuring, and
Diversifying
Main
Contents:
Hedging: Forward (Swap Contract), Future, Matching
Assets to Liability
Insurance: Financial Guarantees, Options
Diversifying: Measures of expected payoffs and
risk (variance), diversifiable risk (firm-specific risk)/
non-diversifiable risk (market risk)
Problems of homework: understand accurately the
meanings of questions and give your answers correctly
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Solutions:
11.1 – Discriminate the proceeds from sale on
spot market and cash flows from future
contract
a. Give the loss or gain (cash flows) from
future contract
b. Give the proceeds from sale of orange on the
spot market
c. After the hedging, the total receipts are fixed
at 250,000
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11.8 –Swap contract is equivalent to a series of
forward contracts
a. Enter into a swap contract with a counterparty
whereby you would agree now to receive or pay each
year an amount of cash equal to 2,700,000,000 yen
times the difference between the 90 yen/dollar forward
rate and spot rate at the time
b. $30,000,000 per year or 2.7 billion yen per year
c. Anyone or any company interested in hedging a
possible appreciation in the dollar versus the yen.
Perhaps a Japanese company with sales in the US
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11.13 –Option is an insuring instrument
a. a call option gives someone rights to buy
something at a promised price (exercise price) in the
future. Note that the option is the right, but not the
obligation to buy or sell, which should be distinguished
from forward /future contract
b. the right is valuable, so you must pay some fee for
the option contract, and the option fee is less than the
change of spot price, that is to say, no one would be
willing to pay a fee that exceeds the difference between
today’s price and next year’s expected price
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Chapter 12: Choosing an Investment
Portfolio
Objective: trade-off between expected return and risk, that is
to say, to offer investors the highest expected rate of return
for the degree of risk they are willing to bear
Process:
Find the optimal combination of risky assets
Mix the optimal risky asset portfolio with the riskless asset
Models and implications of Portfolio Theory:
 William F. Sharpe, Gordon J. Alexander, Jeffery V. Bailey.
Investments. 6th Edition, Prentice Hall, 1995;
清华大学出版社, 影印版, 2001.（Chapter 6 & 7）
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A asset is riskless or risk-free only in term of certain
unit of account and only if held to maturity
Riskless Assets
Risky Assets
Combining: parabola
trade-off line
(minimum-variance portfolio)
Combining: risk-reward trade-off line
(Relationship between the standard
deviation and the expected return)
Combining the riskless
and risky asset
(the tangency portfolio)
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Solutions:
12.3 –The implications and derivation of RiskReward Trade-Off Line
a. the independent variable is Standard
Deviation and dependent variable is
Expected Return
b. Intercept: the return of riskless asset
Slope: extra expected return to investors for
each unit of extra risk that she bears
c. 0.15 = w*return of riskless asset + (1-w)*
expected return of risky asset
w=?
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12.6 & 12.7 – To derive the tangent portfolio and
calculate its expected return and
standard derivation
 Step 1 : derive the weights of risky assets in the
tangent portfolio by formulas on page 332.
 Step 2 : calculate expected return and standard
derivation of tangent portfolio by formulas
on page 329.
 Step 3 : calculate expected return and standard
derivation of any portfolio by formulas on
page 329.
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12.8 – Implications of portfolio selection
 Locations on Risk-Reward Trade-Off Line and
the investment strategies
 The investment strategies and the type or
preference of investor
 This strategy calls for borrowing additional funds and investing
them in the optimal portfolio of AT&T and Microsoft stock. A
risk-tolerant, aggressive investor would embark on this strategy.
this person would be assuming the risk of the stock portfolio
with no risk-free component; the money at risk is not only from
this person’s own wealth but also represents a sum that is owed
to some creditor (such as a margin account extended by the
investor’s broker).
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