Principles of Finance - univie.ac.athomepage.univie.ac.at/natalia.ivanova/wp-content/uploads/...Market order: executed at the best available price Limit order: executed at a price

Principles of FinanceWinter Term 2010

Natalia [email protected]

2

SyllabusPart 1 - Single-period random cash flows (Luenberger ch. 1, 6, 7.1-.7, 8.1-

.4, 9.1-.5, A1-2, B1-3)Stocks (incl. empirical features of returns)Mean-variance portfolio theoryUtility theory“Capital Asset Pricing Model” (incl. performance measurement)Factor models (incl. “Arbitrage Pricing Theory”)

Part 2 - Multi-period deterministic cash flows (Luenberger ch. 3, 4.1-.4, 4.7-.9)

Fixed income securities (incl. credit and market risk)Floating rate notes

Part 3 - Derivative securities (Hull parts from ch. 1-3, 5, 7-11, 13, 15, 17)ForwardsFuturesOptionsSwaps

Midterm

3

Literature

First and Second Part:Investment Science, David Luenberger, Oxford University Press, 1998.

Third Part:Options, Futures, and Other Derivatives, John Hull, 6th edition, Prentice Hall, 2005.

Additional/alternative texts: Haugen, Robert A., Modern Investment Theory; Prentice Hall, 2001.

Levy, Haim and Post, Thierry, Investments, Prentice Hall, 2005.

Grinblatt, M., and Titman, S., Financial Markets and Corporate Strategy, 2nd

edition, 2002.

4

Overview

Financial markets and the firm

Players in financial markets

Products traded on financial markets

Classification of financial markets

Pricing

Introduction to financial markets

5

Financial markets and the firm

Source: Admati (2002)


6

Players in financial markets Borrowers: need funds

Lenders / investors: wish to invest funds

Hedgers: want to reduce risk

Speculators: are willing to take risk

Arbitrageurs: lock in profits by exploiting market inefficiencies Arbitrage opportunity / profit: riskless profit with zero initial

investment Arbitrage strategy: buy cheap and sell expensive

Financial Intermediaries (FI)


7

Players in financial markets: Financial Intermediaries (FI)

Banks: match borrowers and lenders / investors

Ex-post information asymmetry between potential lenders and a risk neutral entrepreneur and costly monitoring ➨ FI (commercial banks) are optimal (least costly alternative) given a “high” number of lenders (see Diamond (1984))

Other FI: Investment banks: help companies to obtain funding directly from

lenders

Brokers: match investors wishing to trade with each other

Market makers: commit to quote prices at which they are willing to buy or sell from or to investors

Insurance companies

Mutual funds


Bonds / fixed income securities deterministic contractual CF stream

classification e.g.

- according to issuer (government bonds and corporate bonds),

- default risk (investment grade, junk bonds, etc.)

Shares (random CFs):

common stock – are securities which entitles their holders to some share in the companies profit. In particular their holders receive dividends. In addition, holders of common stock are able to influence the corporation through voting on establishing corporate objectives and policy, stock splits, and electing the company's board of directors.

Preferred stock usually carries no voting rights, but bear superior priority over common stock in the payment of dividends and upon liquidation.

Currencies / foreign exchange (FX)

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Products traded on financial markets Derivatives: forwards, futures, swaps and options

Forwards-are contracts initiated at one time, performance in accordance with the terms of the contract occurs subsequent time. Price at which exchange occurs is set at the time of the initial contracting.

Futures-are type of forward contract with highly standardized and closely specified contract terms.

Futures always trade on organized markets. Performance is guaranteed by clearing house. They require that traders post sum of money on the margin accounts.

Swaps –are agreements to exchange one cash flow stream for another. There exist interest rate, currency swaps and commodity swaps.

Options-there exist two types of options: calls and puts.

- Calls-are contracts which give a right (not an obligation) to their holders to buy a specified commodity for a specified price at a specified date (European call) or at any time before its expiration (American call).

- Puts-are contracts which give a right to their holders to sell a specified commodity for a specified price at a specified date (European put) or at any time before its expiration (American put). 9

10

Classification of financial markets … according to traded products: stock market, bond market,

derivatives market, FX market, commodities market

… according to the maturity of investments Spot market: trade date ‘equals’ delivery date Future market: trade date ‘before’ delivery date Money market: short-term borrowing (/ - debt financing) and investing Capital market: long-term borrowing (/ - debt financing) and investing

… according to issuance vs. trading of securities Primary market: initial public offerings (IPOs) Secondary market: trading of existing securities

… according to the trading system Organized exchanges: centralized auction-type markets Over-the-counter (OTC) market: network of security dealers who make

markets by taking positions in individual securities on their own account


11

Global volume of financial assets

World GDP 2005,20068: 44.4, 48.4 tr USD (worldbank) Source: SIFMA (2006)

Financial Assets

12

Financial Assets Growth (US)

13

14

Important stock markets

Single-period random cash flows: Stocks

Source: FIBV

Market capitalization in billion USD

Exchange End 1990 End 1995 End 2000 End 2005

NYSE 2692.6 5654.8 11534.6 13310.6Nasdaq 310.8 1159.9 3597.1 3604Tokyo SE 2928.5 3545.3 3157.2 4572.9London SE 850 1346.6 2612.2 3058.2

Deutsche Börse 355.3 577.4 1270.2 1221.1Swiss Exchange 157.6 398.1 792.3 935.4Toronto SE 241.9 366.3 770.1 1482.2

Vienna SE 26.3 32.5 29.9 126.3Ljubljana SE - 0.3 3.1 7.9

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Pricing Supply and demand ➨ price and quantity in an equilibrium

(supply = demand)

What determines the price at which investors are willing to trade? Expectations about future cash flows Timing of these cash flows Riskiness of these cash flows ➨ Present value of future CFs

The usual assumptions Investors prefer more to less Investors are risk averse Investors prefer early consumption to late consumption Investors are rational


16

Overview Types of Trade

Introduction ( review of some statistical concepts calculating returns and discussing empirical features of returns)

Mean-variance portfolio theory

Utility theory

Capital Asset Pricing Model

Factor models

Arbitrage Pricing Theory

Performance measurement


17

Position in Assets Common stocks

… represent partial equity ownership in a company, i.p. residual claim on the earnings of the firm with voting rights

… no maturity date … fluctuating dividend: entirely dependent on firm management

small fraction of earnings as dividends ➨ if the retained earnings are invested profitably, the firm will grow in size ➨ captured by common stockholders through capital appreciation eventually

… liquidation: rights to a company's assets after debt holders and preferred stockholders

Preferred stocks … represent partial equity ownership in a company, i.p. claim on the earnings of

the firm with no voting rights … usually no maturity date but often callable … fixed dividend: paid before any dividends are paid to common stockholders,

unless the company lacks the financial ability to do so: cumulative vs. non-cumulative preferred stocks

… liquidation: rights to a company's assets after debt holders but before common stockholders


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Types of trades

Classification on the basis of the execution price Market order: executed at the best available price

Limit order: executed at a price at least as advantageous as a stated limit price (if the trade can’t be completed at that price, it is delayed until it is possible to execute it under those conditions)

Stop loss order: sell if the price falls below a specified level

Classification on the basis of allowable time for completion Good until canceled: remains indefinitely

Good until date: remains valid until a prespecified date

Good for day / day order: must be executed by the end or the day or it is canceled

Fill or kill order: must be executed immediately or it is canceled


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Types of trades Long position: owning an asset (e.g. 100 OMV shares)

Short position / short selling Borrow shares from someone (the owner) usually through a broker, i.e.

taking a short position

Sell (short) these shares, say for x

Pay dividends to the owner of the shares

Buy shares back, say for y

Return the shares borrowed, i.e. closing out the short position

Profit / loss = x - y - dividends paid

If the owner wants to sell her shares the broker will simply borrow them from some other costumer. However, if there are too many short sales and not enough costumers from whom to borrow shares, the broker may fail to execute the trade (“short squeeze”). In a short squeeze the broker has the right to force us to close out our short position.


20

Computing returns

Simple returns, discrete compounding

Log returns, continuous compounding

Relation between simple and log returns

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Computing returns

Multi-period simple returns

Multi-period log returns

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Portfolio Return

22


Portfolio Return Example: Portfolio Retrurn calculation

To calculate portfolio return we should first determine the fraction of wealth invested in each individual stock. Then multiply them by respective returns and sum up.

23


Some concepts from the probability theory

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Some concepts from the probability theory Consider a random variable which assigns 1,...,6 to the outcomes of the ordinary rolling six-

sided dice. Each outcome is equally likely and each has probability of occurrence 1/6. It is depicted on the following graph:

Normal Distribution

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Some concepts from the probability theory

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Operations on Distribution Parameters

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Some statistical concepts (Arithmetic) Mean

(Sample) Variance, (sample) covariance, and (sample) correlation

(Sample) Skewness: measure for symmetry<0 negatively skewed, =0 symmetrical, >0 positively skewed

(Sample) Kurtosis: measure for tail behavior<3 polykurtic, =3 like normal distribution, >3 leptokurtic (“fat tails”)

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Some statistical concepts Jarque-Bera test for normality

(Sample) Autocovariance: measure for linear temporal dependencies between time t and time t-k

(Sample) Autocorrelation / - serial correlation

If a time series is uncorrelated (ck=rk=0, "k ), it is called a white-noise process

Significant autocorrelation in squared or absolute returns is evidence for time-varying variance (“heteroskedasticity”) (fl standard errors must be adjusted)

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20

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30

Empirical features of returns

Often assumed that returns follow a normal distribution (central limit theorem, convenience) ➨ Then prices must be lognormally distributed

But: In empirically, returns aren’t exactly normal distributed!- Skewness ≠ 0 - Kurtosis ≠ 3, usually kurtosis > 3 (“leptokurtic”, i.e. the distribution is

more strongly concentrated around the mean than the normal and assigns correspondingly higher probabilities to extreme values; fat tails)


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Empirical features of returns

Simple and log returns cannot be distinguished in such graphs

Erratic (“white noise”), strongly oscillating behavior of returns around the more or less constant mean (“stationary process”; “mean reverting”)

Variance / volatility (standard deviation) is not constant over time (“heteroskedasticity”). We have periods of different length with approximately the same degree of variation (“volatility clustering”)


Hystorical Returns

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1920 1930 1940 1950 1960 1970 1980 1990 2000 2010-60

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StocksT billsT bonds


Arithmetic Average Stocks T Bills T Bonds

1928-2009 11,27% 3,74% 5,24%

1960-2009 10,81% 5,33% 7,03%

2000-2009 1,15% 2,74% 6,62%

Converting yearly parameters into monthly counterparts

33


34

Overview

Portfolio return

Portfolio risk

Combination lines (incl. diversification)

Minimum variance and efficient set (Markowitz and Tobin)

Single-period random cash flows: Mean-variance portfolio theory

35

Portfolio return

Recall portfolio return formula

Expected return of a portfolio

Expected value of a portfolio is a weighted average of expected returns of individual assets, where weights reflect share of total wealth invested in a particular security.

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36

Portfolio risk We quantify risk in terms of statistical measures, conventionally this is

done using the variance / standard deviation (volatility)

Variance of a portfolio (random variable)

Covariance and correlation of two random variables

Variance of a weighted sum

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37

Properties of portfolios: risk

Multiple-asset portfolio

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38

Examples An investor has € 1000. Hearing from an investment opportunity with an

expected rate of return of 24%, she sells short another security with an expected return of 5% for € 4000 and invests all his money in the other security. What is the expected rate of return on the portfolio?

Given are two uncorrelated securities: Stock A with E(r)=12%, SD(r)=8% and stock B with E(r)=2%, SD(r)=10%. Calculate the expected rate of return and standard deviation for a portfolio of € 15000 long in A and € 5000 short in B.


39

Properties of portfolios: diversification

Diversification: strategy designed to reduce risk by spreading the portfolio across many assets

Unique risk / unsystematic risk / diversifiable risk / idiosyncratic risk: risk factors affecting only that firm

Market risk / systematic risk: economy-wide sources of risk that affect the overall stock market


05 10 15

Number of Securities

Port

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Market risk

Uniquerisk

40

Properties of portfolios: diversification

Naive diversification: portfolio with n assets, each asset has weight 1/n

Example (2 years of recent weekly data): naive portfolios of Austrian stocks


Boehler Lenzing Mayr MK Erste EVN Return # SD100.00 0.033 1 0.219 50.00 50.00 0.106 2 0.145 33.33 33.33 33.33 0.117 3 0.145 25.00 25.00 25.00 25.00 0.153 4 0.135 20.00 20.00 20.00 20.00 20.00 0.140 5 0.121

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Principles of Finance - univie.ac.athomepage.univie.ac.at/natalia.ivanova/wp-content/uploads/...Market order: executed at the best available price Limit order: executed at a price