BUS316 Derivative Securities
Instructor: Ming Li
Introduction
Function of financial markets
Financial markets bridge the demand and supply of capital, and aid the resource allocation process for the economy
Provide a place for exchanging assets
Provide liquidity
Determine the price of assets
Market efficiency
Price efficiency: prices reflect the true values of assets Weak efficiency: current prices reflect information
embodied in past price movements Semi-strong efficiency: current prices reflect information
embodied in past price movements and all public information
Strong efficiency: current prices reflect information embodied in past price movements and all public and private information
Operational efficiency
Transactions occur accurately Fees reflect true costs of providing services
Type of financial instruments
Financial assets are intangible: contracts that specify the legal claim to future cash flows
Fixed income, debt instruments Loan, bond, money market instruments
Equity Common shares, stock
Hybrid/intermediate instruments Preferred share, convertible bonds
Derivatives Futures and forwards, swaps, options
What is a derivative security?
It is a financial contract between two parties.
Its value is contingent on the value of some basic asset
The basic asset is called the underlying asset
A derivative can be viewed as a bet on the behaviour of the underlying assets
It can also be viewed as an asset that entitles you to some payments over the relevant time interval.
An example
An iPad is not a derivative
Leo and Jan agree: in 6 months, if iPad price goes up, Leo pays Jan $50; if iPad price drops, Jan pays Leo $50.
This agreement is a derivative
Underlying asset: iPad
Examples of underlying assets
Stocks, stock index
Bonds
Commodities: gold, silver, grain, etc.
Energy: crude oil, natural gas, etc.
Exchange rates
Interest rates
among others
Source: McDonald, 2006
Why derivatives
Fundamental economic idea: existence of risk-sharing mechanisms benefits everyone
Illustrate in the iPad example
Leo owns a shop and sells iPad; Jan plans to buy an iPad in 6 months
1970s witnessed increase in price risk, as well as spectacular growth in derivative market
Use of derivatives
To Speculate
Bet on the future direction of market
For example
A: An asset. An
investor believes that price of A is
going up over the
next month
B:
A derivative on asset A;
Bs value increases as
price of A increases
Invest in B:
to speculate on a rise in
As price
Use of derivatives
To Hedge
Reduce risk
For example
A:
An risky asset - value of A
may decrease
B:
A derivative; Bs value
increases as value of A decreases
Holding A and B together:
B hedges against the
price risk of A
To Arbitrage
Make riskless profit
For example
Use of derivatives
Where are derivatives traded
Organized exchanges
Canada: Montreal Exchange
US: CBOE, CME
UK: LIFFE
Asia: HKFE, TFX, CFFEX
Alternative to exchanges
Over-The-Counter (OTC) market
Market size of derivatives markets
Countries: G10+2; Source: www.bis.org
0
100000
200000
300000
400000
500000
600000
700000
800000
No
tio
nal
Pri
nci
pal
, bill
ion
US
Market Size, Exchange vs OTC
OTC
Exchange
Review: Time value of money, Interest Rates
Hull Ch 4.1-4.3, 4.6
Growth and discounting concept
Investing PV at some rate R over some time period T gives FV
R may be called rate of return, discount rate, or interest rate (for lending/borrowing)
PV FV
growth
discount Time
Growth and discounting
r: effective rate per period
T: number of periods
T
T rPVFV
rPVFV
)1(
)1(1
T
T rFVPV
rFVPV
)1(
)1(1
and
Growth and discounting
R: rate per annum
m: compounding frequency per annum
n: investment duration in years
m infinity: continuous compounding
nm
nm
RPVFV )1( nmn
m
RFVPV )1(and
nR
n ePVFV nRn eFVPV
and
Effect of compounding frequency
A = $100, R = 10%, n = 1 yr
Compounding Frequency Terminal Value of Investment
Annually, m=1 110.00
Semi-annually, m=2 110.25
Quarterly, m=4 110.38
Monthly, m=12 110.47
Weekly, m=52 110.51
Daily, m=365 110.52
Continuously, m=infinity 110.52
Hull, Table 4.1
Effect of time
Frank put away $2k each year into a TFSA from age 23 to 28, earning 12% per year
Steve put away $2k each year into a TFSA from age 29 to 60, earning 12% per year
$-
$100,000.00
$200,000.00
$300,000.00
$400,000.00
$500,000.00
$600,000.00
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Frank
Steve
At age 60, Frank had $609,900 Steve had $609,600
Frank Steve 23 2000 24 2000 25 2000 26 2000 27 2000 28 2000 29 2000 30 2000 31 2000 32 2000
58 2000 59 2000 60 2000
$ 12,000 $ 64,000
Equivalent rates
R1 and R2 are equivalent if they give the same terminal value for the same initial investment. In this case, R1 and R2 are called equivalent rates.
An example
ABC bank offers you an investment plan, paying 5% interest per annum with semi-annual compounding
XYZ bank also offers you an investment plan, paying continuously compounded interest
What rate should XYZ bank pay to make its investment plan more appealing to you?
Interest rate
Interest rate defines the amount of money a borrower promises to pay the lender, besides the repayment of principal amount.
Interest rates depend on
Credit risk: the risk that the borrower may default and fail to pay interest and principal to the lender
Term-to-maturity: how long to borrow for
Type of interest rates
Three benchmark interest rates
Treasury Rates
Rates on Treasury bills and Treasury bonds
Borrower: a government; Lender: investors
Denomination: in a governments own currency
Terms: short (month) to long (10+ years)
Usually considered credit risk-free
Type of interest rates
Three benchmark interest rates LIBOR
London Inter-Bank Offered Rate
Quoted by a bank (lender), the rate at which it is willing to make a large deposit at other banks (borrower)
Denomination: in all major currencies
Terms: overnight to 12-month
Borrowing banks must have AA credit rating
Usually considered very close to credit risk-free
In practice, LIBOR is preferred over Treasury rates when pricing derivatives
Type of rates
Three benchmark interest rates
Repo rate
Repurchase agreement: Borrower sells securities to lender and buy the securities back later at a slightly higher price
The difference between the selling price and the repurchase price is the interest earned by lender repo rate
Considered as borrowing with the securities as collateral
Terms: overnight (most common) and others
Zero rates
n-year zero coupon rate: interest rate (per annum) earned on an investment that 1. Starts today and lasts for n years
2. Pays no coupon or intermediate payments; principal and interest are paid at the end of n years
Also called: n-year spot rate, n-year zero rate, or n-year zero.
An example
Suppose the current 1-year, 3-year, and 5-year zero rates are 1%, 3%, and 5%. Rates are per annum, and continuously compounded.
You invest $1000 in a 5-year zero coupon bond. How much will you get in 5 years?
You want to have $5000 in 3 years. How much do you need to invest in the 3-year zero coupon bond today?
Forward rates
Forward rates are interest rates for investments that are arranged today but do not start until some time in the future
They are implied by current zero rates
Forward rates Year (n)
n-year Zero rate
nth year Forward rate
1 3.0%
2 4.0% 5.0%
3 4.6% 5.8%
2-year zero rate is 4%. It means: at beginning of yr 1 invest $100 for 2 years, get $100 x e4% x 2 = $108.33 at end of yr 2
2nd year forward rate is 5%. It is the rate earned during yr 2, implied by the zero rates; as if at beginning of yr 1 invest $100 for 1 year, get $100 x e3% x 1 = $103.05 at end of yr 1; then at beginning of yr 2 invest $103.05 for 1 year, get $103 x e5% x 1 = $108.33 at end of yr 2
With continuous compounding, n-year zero rate is the average of 1st to nth year forward rates (actually, there is no such 1st year forward rate; it is the same as 1-year zero rate)
Forward rates
With continuous compounding, forward rate RF between T1 and T2 can be calculated using T1-year zero rate, R1, and T2-year zero rate, R2
1
1
2
1122
2
1122
)(TT
TRRRR
or
TT
TRTRR
F
F
Yield curve
plot zero rates against the term-to-maturity Each yield curve is at a particular point in time, for debt of a particular
borrower in a particular currency
This relationship between interest rate and term-to-maturity is known as the term structure of interest rates
0
0.005
0.01
0.015
0.02
0.025
0.03
zero
rat
es
Term (in years)
Canadian Treasury Yield Curve (Jan 15, 2013)
source: Bank of Canada
4-year zero rate: 1.40% 19-year zero rate: 2.59%
Shape of yield curve
Yield curves tend to slope upwards, but it can be downward sloping some time.
3 alternative theories to explain
0.089
0.09
0.091
0.092
0.093
0.094
0.095
0.096
0.097
0.098
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75
Zero
Rat
e
Term (in years)
Canadian Treasury Yield Curve (Jan 2, 1986)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75
Zero
Rat
e
Term (in years)
Canadian Treasury Yield Curve (Jan 15, 2013)
Shape of yield curve
3 alternative theories
Expectations theory
Long term interest rates reflect expected future short-term interest rates
nth year forward rate is equal to the expected zero rate for that period
Shape of yield curve
3 alternative theories
Market segmentation theory
Short-, medium-, and long-term borrowing/lending markets are different debt markets; so rates in each market are determined by the supply and demand in that market
No necessary relationship between short-, medium- and long-term interest rates
Shape of yield curve
3 alternative theories
Liquidity preference theory
Investors prefer liquidity and invest funds for short periods of time; borrowers prefer to lock in funds for long periods of time
As a result, investors need to be compensated for long-term lending; long-term rates should be higher than short-term rates; yield curves are generally upward sloping