BUS316 Derivative Securities

Instructor: Ming Li

mla70@sfu.ca

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