Principles of Finance - Exeterpeople.exeter.ac.uk/wl203/BEAM010/Materials/Lecture 1/PoF 2004... · 9E. Elton, M. Gruber, S. Brown, W. Goetzmann, Modern Portfolio Theory and Investment

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Principles of Finance - Lecture 1 1October 5, 2004

Principles of Finance

Grzegorz Trojanowski

Lecture 1:Introduction and preliminary concepts


Required course reading

• Core textbook:E. Elton, M. Gruber, S. Brown, W. Goetzmann,

Modern Portfolio Theory and Investment Analysis, 6th edition, Wiley

• Other reading:Assigned papers (details TBA)

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Optional course reading

• Supplementary textbook reading:D. Blake, Financial Market Analysis, 2nd edition,

McGraw HillD. Luenberger, Investment Science, OUPW. Sharpe, G. J. Alexander, J. V. Bailey,

Investments, 6th edition, Prentice HallG. J. Alexander, W. Sharpe, J. V. Bailey, Fundamentals of Investments, 3rd edition, Prentice Hall

• Other supplementary reading:Assigned papers (details TBA)


Lecture 1 material

• Required reading:Elton et al., Chapters 1, 2, 3, 4

• Supplementary reading:Blake, Chapter 1Luenberger, Chapters 1 and 6 (Sections 6.1-6.4)Sharpe et al., Chapters 1-3

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Lecture 1: Checklist

• By the end of this lecture you should:Be familiar with the different types of financial markets, market participants, and financial securities Be able to compute the holding period return on a

securityBe able to compute the expected return, variance, and standard deviation of returns for a single securityBe able to compute the covariance and correlation coefficient between the returns of two securities


Components of financial market

• Participants• Market and trading mechanisms• Regulatory framework• Securities

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Market participants (1)

• End users:LendersBorrowers

• Brokers:Act as agents for end usersProfit through a commission or feeDo not trade for their own account

• Dealers:Trade for their own accountProfit through bid-ask spread or through speculation


Market participants (2)

• Arbitrageurs:Exploit differences between the actual price of a security and its

fair value (or fundamental value) or between the prices of a single security quoted in two different markets

• Hedgers:Remove price uncertainty by investing in securities whose prices

are correlated with securities they own now or expect to own in the future

• Speculators:Profit (or lose) by exploiting their view of how prices will move

in the future

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Types of market (1)

• Primary vs. secondary markets:

The primary market is the market for new securities issued by companies and governments

The secondary market is the market for previously issued securities


Types of market (2)

• Money vs. capital markets:

The money market is the market for short term liabilities, usually with maturities of less than 1 year

The capital market is the market for long term securities, usually in excess of one year

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Types of market (3)

• Physical vs. over-the-counter (OTC) markets:

Physical markets occupy a physical location, usually a trading floor, where buyers and sellers meet in person

OTC markets are geographically dispersed markets, where buyers and sellers ‘meet’ over the telephone or by computer


Types of market (4)

• Call markets vs. continuous markets:

In a call market, trading takes place at specified time intervals

Continuous markets are markets are markets where trading takes place on a continuous basis

Sometimes a combination of the two, e.g. NYSE, where market opens like a call market and becomes a continuous market afterwards

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Types of market (5)

• Dealer markets vs. broker marketsIn a broker market, the broker acts as an agent an

for an investor and buys or sells securities on the investor’s behalf (i.e. security holders are trading with other shareholders albeit utilising the agent)In a dealer market, the dealer purchases or sells securities for the investor utilising dealer’s own inventory


Types of market (6)

• Trade executionThe markets where the trading is executed electronically The markets where the execution of trading involves people

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Types of securities

• Fixed income securities• Equities• Derivatives


Fixed income securities (1)

• Fixed income securities offer a contractual claim, or stream of claims, against the issuer

• Short term fixed income securities are traded in the money market and are known as money market instruments

• Money market instruments involve a single payment at maturity, known as the principle or face value, and are sold at a discount

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• Longer term fixed income securities are traded in the capital market and are known as bonds

• A bond typically offers a series of regular smaller claims, known as coupons, followed by a larger terminal payment

• The maturity of a fixed income security may be as little as several hours and, as much as 50 years, or indefinite



• Fixed income securities are issued by domestic and foreign governments, public authorities, and private corporations

• Failure to honour fixed income securities results in default, or bankruptcy, for the issuer

• In case of the issuer’s default, the holder of the fixed income security will receive less than the promised claim, and possibly nothing

• The likelihood of default for corporate fixed income securities varies widely

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Equities (1)• In contrast to fixed income securities, equities (or

shares, or stocks) represent a residual claim on the issuer

• The holder of equity receives a dividend payment only after all other claimants have been paid

• Although holders of equity have only a residual claim over company’s earnings, the size of this claim is unlimited

• If the company does better than expected then it is the company’s equity holders – not its bondholders – that benefit


Equities (2)

• Preferred stock is equity that promises a dividend payment

• However, unlike for bonds, failure to pay dividends of a preferred stock does not result in bankruptcy, but instead the unpaid dividends accumulate

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Derivatives (1)

• Derivatives (or contingent claims) are securities whose value depends on the value of some other security

• Derivatives serve a number of purposes, but primarily they facilitate speculation and hedging

• Derivatives include forwards, futures, options, and swaps

• Some fixed income securities have derivative features


Derivatives (2)• A forward is an agreement to buy or sell the underlying

asset (security) at some future date, and are usually tailor made arrangements between private individuals and/or institutions

• A future is also an agreement to buy or sell the underlying asset (security) at some future date, but unlike a forward, is traded in standardised contracts on the exchange

• Futures contracts operate using a system of marking to market, whereby any profit or loss accruing to the futures contract is settled on a daily basis

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Derivatives (3)

• An option gives the right – but not the obligation – to buy or sell the underlying asset (security) at some future date

• A swap is an agreement to swap the cash flows on two obligations


Risky and risk free securities (1)

• Default free government bond:

If the government bond is held until maturity then the return that the investor receives – both coupon and capital gain – is riskless

If the government bond is sold before the maturity then the return the investor receives is risky, since the sale price of the bond – and hence the capital gain component of the return – is uncertain

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• Corporate bond:

If the corporate bond is held until maturity then the return is risky since there is some chance that the issuer of the bond may default, and so the redemption value and the coupon payments are uncertain

If the government bond is sold before the maturity then the return the investor receives is risky, since the sale price of the bond – and hence the capital gain component of the return – is uncertain



• The return that the investor receives when holding the equity is risky since both the dividend payments and the sale price of the equity are uncertain

• Thus, the only risk free security is a default free government bond that is held until maturity

• All other financial securities are risky securities

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Holding period return (1)• Consider a non-dividend paying stock whose value is

pt at time t and pt+1 at time t+1• The holding period return on such a stock is defined

as

• If the stock pays dividend of dt+1 at time t+1then the holding period return is given by

t

ttt p

ppR −= +

+1

1

t

t

t

tt

t

tttt p

dp

ppp

dppR 11111

+++++ +

−=

+−=


Holding period return (2)• The holding period return therefore comprises two

components:

Capital gain, which is the change in the price of security between when investor buys the security and when he or she sells the security, or when it is redeemed by the issuer

Dividend yield, comprising the cash payments made to the investor while he or she is the owner of the security, such as equity dividends and bond coupons

• The formula for the holding period return implicitly assumes that compounding takes place only once at the end of the period

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Continuously compounded returns

• Typically in finance, we use continuously compounded returns, or log returns, defined as:

• It the stock pays dividends then the continuously compounded return is given by

• For dividend paying stocks and stock indices, data is often provided in the form of a total return index that reflects both the price of the security and the accumulated dividends that it pays

ttt

ttt pp

ppRr lnlnln)1ln( 1

111 −=⎟⎟

⎠

⎞⎜⎜⎝

⎛=+= +

+++

tttt

ttt pdp

pdpr ln)ln(ln 11

111 −+=⎟⎟

⎠

⎞⎜⎜⎝

⎛ += ++

+++


Calculation of returns: Excel example

4.03%3.93%4.12%4.01%3149.8503.2Mar-9510

0.10%2.81%0.10%2.85%3025.3483.8Feb-959

-2.00%1.70%-1.98%1.71%3022.2470.4Jan-958

1.63%2.23%1.64%2.25%3083.4462.5Dec-947

0.13%-2.95%0.13%-2.91%3033.5452.3Nov-946

0.70%0.82%0.70%0.82%3029.6465.9Oct-945

3008.5462.1Sep-944

FTSE100S&P500FTSE100S&P500FTSE100S&P500Date3

Compounded ReturnsMonthly ReturnsReturn Index2

Continuously1

GFEDCBA

=(B5-B4)/B4 =LN(C5/C4)

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Returns as random variables (1)

• At the beginning of the period, pt is known but, for a risky security, pt and possibly dt are unknown

• Therefore the return on a risky security can be considered a random variable, drawn from a probability distribution

• The probability distribution tells us the probability of achieving a particular return in a particular range

• If we consider the security in isolation, then we use its marginal probability distribution



• The marginal distribution is simply the function that gives the probability associated with different return outcomes, irrespective of the returns of other securities

• Two important characteristics of the marginal probability distribution of returns are the expected return and the variance of returns

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• Alternatively, if we consider a number of securities simultaneously, we use their joint probability distribution

• The joint probability distribution of returns tells us the probability of a particular return on one security, given a particular return on another security

• The joint density is characterised by the covariance or correlation of returns


Expected return • The first characteristic of a return distribution is its

expected value, or expected return, denoted E(R)• The expected return of a security is simply the mean of

the marginal probability distribution• The expected return is a measure of the ‘average’ return• The true return distribution is unobservable and so the

population expected returns are unknown• However, we can estimate it from a sample of returns

{rt_, t = 1, …, T}, using the sample mean, denoted___or__, and computed as

µ̂r

∑==

T

ttrT

r1

1

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Expected return: Excel example

4.03%3.93%10

0.10%2.81%9

-2.00%1.70%8

1.63%2.23%7

0.13%-2.95%6

0.34%0.73%Mean0.70%0.82%5

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FTSE100S&P500FTSE100S&P5003

Compounded Returns2

Continuously1

LKJIHGF

=AVERAGE(F5:F124)


Variance of returns (1)

• The variance measures the average squared difference between each return and the mean return

• The variance is a measure of the ‘dispersion’ or ‘spread’ of returns

• The more dispersed the returns are, the further on average they will be from their mean, and so the higher the variance

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Variance of returns (2) • Again, since the true probability distribution is

unobserved, the population variance is unknown• However, we can estimate it from a sample of returns

using the sample variance, computed as

• Sometimes the divisor (T – 1) is used instead of T, but in large samples this will not make (much) difference

• The units of variance is (returns)2

• Often, a more useful measure is the standard deviation of returns, which is the (positive) square root of the variance

∑ −==

T

tt rr

T 1

22 )(1σ̂

σσ =+= 2)(rSD


Variance of returns: Excel example

4.03%3.93%10

0.10%2.81%9

-2.00%1.70%8

4.50%4.84%Standard Deviation1.63%2.23%7

0.00200.0023Variance0.13%-2.95%6

0.34%0.73%Mean0.70%0.82%5

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Compounded Returns2

Continuously1

LKJIHGF

=VARP(F5:F124)

=STDEVP(F5:F124)or

=SQRT(K6)

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Covariance of returns

• The joint probability distribution is characterised by the covariance of returns

• The covariance of returns measures the linearassociation between two return series, i.e. the extent to which they move together

• We can estimate the covariance of returns using the sample covariance computed as

∑ −−==

T

tBtBAtABA rrrr

T 1,,, ))((1σ̂


Covariance of returns: Excel example

4.03%3.93%10

0.10%2.81%9

0.0018Covariance-2.00%1.70%8


0.00200.0023Variance0.13%-2.95%6

0.34%0.73%Mean0.70%0.82%5

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Compounded Returns2

Continuously1

LKJIHGF

=COVAR(F5:F124,G5:G124)

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Correlation coefficient (1) • The covariance, like the variance, depends on the units

of measurement of the data• In order to know whether the covariance between two

securities is ‘large’ or ‘small’, we need to know what their respective variances are

• It is therefore often useful to normalise the covariance by the square root of the product of the variances of two securities

• The correlation coefficient is defined as

• Again this can be estimated using sample data on two return series

BA

BABA σσ

σρ ,

, =


Correlation coefficient (2) • By construction, the correlation coefficient must lie between -1

and +1• A correlation coefficient equal to +1 means that the two

securities are perfectly positively correlated• A correlation coefficient equal to -1 means that the two

securities are perfectly negatively correlated• A correlation coefficient equal to 0 means that the two

securities are uncorrelated: a change in the price of one security tells us nothing about the change in the price of the other security

• The square of the correlation coefficient is the coefficient of determination or R-squared which measures how much of the variation in one variable is ‘explained’ by the variation in the other variable

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Correlation coefficient: Excel example

67.83%R-Squared4.03%3.93%10

0.8236Correlation0.10%2.81%9

0.0018Covariance-2.00%1.70%8


0.00200.0023Variance0.13%-2.95%6

0.34%0.73%Mean0.70%0.82%5

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Compounded Returns2

Continuously1

LKJIHGF

=K9^2

=CORREL(F5:F124,G5:G124)or

=K8/(K7*L7)

Principles of Finance Week 2: October 12, 2004

Tutorial problems

Problem 1

A. What are the main types of financial securities and how do they differ?

B. A convertible bond is issued to investors who, on a pre-determined date, can convert

their bond into shares in the company. Is a convertible bond debt, equity, or a

derivative? Explain.

C. What are the formulas for the mean and standard deviation of the returns of an asset, and

the covariance and correlation between the returns of two assets?

D. The covariance and the correlation coefficient are two measures of dependence of

random variables. List main differences between those two measures.

Problem 2

• EGBG Chapter 4, Exercise 1, Questions A and B (Questions C and D will be dealt with

during tutorial sessions in Week 4), p. 64-65

Problem 3

• EGBG Chapter 4, Exercise 2, Questions A-D (Question E will be dealt with during

tutorial sessions in Week 4), p. 64-65

Documents

Principles of Finance - Exeterpeople.exeter.ac.uk/wl203/BEAM010/Materials/Lecture 1/PoF 2004... · 9E. Elton, M. Gruber, S. Brown, W. Goetzmann, Modern Portfolio Theory and Investment