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Ch 1: BASIC CONCEPTS IN FINANCE

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Finance is the study of how resources are

valued and allocated in time.

Outcomes of financial decisions are

spread out over time and

not known with certainty in advance

Three key concepts in finance are :

Time value of money

Asset Valuation

(stocks, bonds, derivatives,...)

Risk management

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1.1: Interest and return

Income almost never matches consump-

tion desires exactly.

Either one will need to borrow to pur-

chase more than one can afford or save

excess income.

Costs / benefits of financial decisions arespread over time.

So one needs to compare values of cash-

flows which mature at different times.

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Time value of money: 1ZAR in the hand to-

day is worth more than the expectation of

1ZAR in the future.

Why?

Opportunity cost: To give up consump-

tion of your 1ZAR today, you would ex-

pect to be rewarded with a greater amount

in the future; the promise of consumption

at a higher level in the future motivates

one to save. The desire to receive surplus

on savings leads to an interest rate called

the pure time value of money.

Inflation: Prices of goods rarely stay the

same over time. The purchasing power of

1ZAR now is (usually) greater than 1ZAR

later. Investors expect a higher rate of

return to compensate for inflation.

Uncertainty: One may not receive the

expected sum - this is referred to as in-

vestment or credit risk.

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Opportunity cost: Pure time value of

money give rise to pure rate of interest.

Inflation: The rate of interest on top ofthe rate of inflation is the nominal risk-

free rate.

Uncertainty: The excess amt added to

the nominal risk-free interest rate is the

risk premium.

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1.1.1: Interest

Borrowing is not free: borrower pays premiumfor sum of money from lender.

The cost of borrowing is interest.

Interest rates are not necessarily fixed

- they vary at different times

- different rates may be charged for dif-

ferent durations of lending

Magnitude of interest depends on

- economic factors [inflation; growth rate

of economy, money supply, trade deficits,...]

- credit rating of borrower [government as

a borrower usually pays the lowest interest

rate (treasuries/gilts); non-investment grade

bonds (junk bonds) have highest pre-

miums; the difference or spread reflects

default probabilities].

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Types of interest

For simplicity, assume interest rates are con-stant.

PT denotes the future value at time T of

P0 invested at time 0:

PT = F V(P0).

P0 is the present value of PT:

P0 = P V(PT).

Computing present values is referred to as

discounting and the interest used is referred

to as the discount rate.

Computing future values is referred to as com-

pounding.

PV and FV make it possible to compare dif-

ferent cash flows at different times.

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Simple interest :

Invest P0 at (annual) rate r for time T

years. Then

PT = P0(1 + rT).

Discretely compounded interest:

Invest P0 at (annual) rate r, compounded

n times annually for 1 year. Then

P1 = P0(1 + rn)n.


n times annually for time T years. Then

PT = P0(1 +r

n

)nT.

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Continuously compounded interest:


continuously for time T years. Then

PT = P0erT.

Here we are using limn

(1 + xn)n = ex.

For compound interest, the expectation

of receiving an amount K at a future date

has a value today of:

P V(K) = KerT.

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What is the present value of an invest-

ment that will pay R1000 per year for 5

years given an annual rate of interest of

8.5% per annum (p.a.)?

P V =5

n=1

1000

1.085n

= 10001 1.0855

0.085

= 3940.64.

The investment is less than R4000 - it

is worth no more than R3940.64 at the

given interest rate.

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Which is better: an investment which of-

fers 8.5% or one which offers 8.4% con-

tinuously compounded?

Finding the continuously compounded rate

rc which corresponds to 0.85% semi-annually:

erc = (1 +0.085

2)2

rc = 0.0832

i.e. rc = 8.32%.

Thus, the continuous rate of 8.4% is bet-

ter.

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1.1.2: Returns

Returns are similar to interest rates. The

main difference is that interest rates arepromised and predictable returns on de-

posits, while returns on other assets (e.g.

stocks) are generally uncertain.

Shares are riskier investments than de-posits. expected return on a share

should be greater than the interest of-

fered by a bank.

NB: returns can be negative; interest rates

must be positive (?!)

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Returns

Roughly, the return on an investment is

measured by:

return =

final value + interim cashflows - initial valueinitial value

Mean rates of return are computed for in-

vestments spread over several years. An-

nual rates of return vary.

Suppose the return for year 1 of an in-

vestment is r1 = 30% and for year 2 is

r2 = 42.857%.

The arithmetic mean return is

r = (r1 + r2)/2 = 6.42857%.

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But it would be wrong to assume that an

initial wealth of P0 = R100 will become

P2 = W0 ( 1 + r)2 = R113.27.

In fact

P2 = P0(1 + r1)(1 + r2)

= 100 0.7 1.42857 = R100.

The geometric mean return satisfies

(1 + rg)2 = (1 + r1)(1 + r2) = 1,

i.e. for this example rg = 0%.

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Generalising,

(1 + rg)n = (1 + r1)(1 + r2)...(1 + rn)

and

Pn = P0(1 + rg)n.

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Shares with greater expected return are

considered riskier than shares with lower

expected return:

If 2 shares had the same risk and one of

them had greater return than the other,

then everyone would buy the share with

greater return; this would push up its price

and reduce its return.

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Risk is measured by volatility: this is thestandard deviation of returns.

Returns may be measured as both con-

tinuously and discretely compounded

Returns on bonds are referred to as yields.

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A fundamental relationship in finance:

E[return] = f(risk),

where f is an increasing function. The risk

premium E represents a composite of uncer-

tainties such as business risk, financial risk,

liquidity risk, exchange rate risk, credit risk,

country risk, operational risk, regulatory risk,

...

See also The 100 risks in financial services

by H.-U. Doerig, (2001): Operational Risksin Financial Services, Credit Suisse Group.

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1.2: Markets and instruments

Securities are contracts for future delivery

of goods or money, e.g. shares, bonds,

derivatives.

Shares, bonds, currencies, interest ratesand indexes are examples of primary or

underlying instruments.

A derivative is an instrument whose value

depends on the value of some underlyingasset - forward, contracts, futures, op-

tions and swaps are examples of deriva-

tives.

There is a distinction between primary

and secondary markets. Securities are is-

sued for the first time on a primary market

and are then traded a secondary market -

the latter provides liquidity.

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Borrowing takes place in fixed-income mar-

kets; the money-market is for very short-

term debt (1 yr ).

There is a distinction between the spot

market and the forward market: most trans-

actions are spot transactions (pay now

and receive goods now); to hedge or spec-

ulate on future values, it is possible to sellgoods for delivery in the future by means

of forward and future contracts.

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Equity refers to stocks or shares which

represent ownership of a small piece of

a company. Shareholders own a corpora-tion, while directors (are supposed to) act

in the shareholders best interest; public

limited companies are listed on a stock

exchange - the ownership of such com-

panies are easily transferred, the share-

holders share the profits but have limited

liability - at most they can lose is there

investment.

Most shares pay regular dividends - the

amount varies depending on profitability

and opportunities for growth - a share

may be bought cum- or ex-dividend; on

the ex-dividend date, the share price de-

creases by the amount of the dividend

Occasionally a company may announce a

stock split: after a 4-for-1 stock split, the

single stock priced at R1 000 is converted

to four shares each valued at R250.

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You can sell a share which you dont own!(in the hope that it can be obtained later

at a cheaper price) - a broker borrows

the share from a client, you sell it and

later buy it in the market to return it to

the broker who, in turn, returns it to the

client. Any dividends that were issued in

the interim are paid to the original owner.

Commodities are raw materials such as

metals, oil, agricultural products, etc ....

These are often traded by speculators who

have no need for the material but who are

betting on future price movements - this

sort of trading is done (indirectly) in the

futures market and contracts are closed

before delivery date.

Currencies are traded on forex markets.

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Indices: an index tracks the changes in ahypothetical portfolio of instruments. A

typical index consists of a weighted sumof a basket of representative stocks. Theserepresentatives and their weights are notnecessarily fixed. E.g. S&P500, DJIA,FTSA100, DAX-30, NIKKEI225.

The most popular SA indices include

ALSI (All share index). This consistsof all shares on the JSE (bar about100, these being, for example, pyra-mids or debentures)

TOPI (Top 40 listed companies index).

Until June 2002 called the ALSI40.

INDI25 (Top 25 listed industrial com-panies index)

FINI15 (Top 15 listed financial com-

panies index)

RESI20 (Top 20 listed resources com-panies index)

Main SA derivatives indices are the TOPI,INDI25.

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Fixed income securities include bonds, notes,

bills. These are debt instruments and

promises to pay a certain rate of interest

which may be fixed or floating. E.g. a

10-yr, %5 semi-annual coupon bond with

a face value of ZAR 1m promises to pay

R25 000 every 6 months for 10 yrs and

a lump-sum of ZAR 1m at the end of the

10-yr period.

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LINKS to explore

http://www.jse.co.za

http://www.bondexchange.co.za

http://www.safex.co.za

http://www.satrix.co.za

History & development of the JSE

http://www.jse.co.za/informational/ his-

toryofjse/history.htm

Understanding Financial Markets & Instru-

ments by Braam van den Berg,

http://www.eagletraders.com/books/afm/

afm0.htm

See Chapter 1, Introduction to the Finan-

cial Markets and Chapter 2, The Equity

Market for notes on the SA Markets and

Market instruments.

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Ch 2: Derivatives

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A derivative security is a financial con-

tract whose values is derived from an un-

derlying variable, such as a stock price,

the level of an index or an interest rate.

Examples:

- a stock options value depends on the

value of the underlying stock;

- the price of a zero-coupon bond depends

on the prevailing interest rate

- the profit/loss made by buying oil fu-

tures depends on the changes in the spot

price for oil.

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Reasons for using derivatives

Hedging and speculation: derivatives are

tools for transferring risk - hedgers wish

to reduce risk while speculators want to

take on more risk in anticipation of greater

rewards

Arbitrageurs seek low risk profits by en-

tering into off-setting positions in differ-

ent markets or instruments.

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2.1: Forwards and futures

A forward contract is an agreement to

buy or sell an asset S (the underlying) at

a certain date T (delivery date, maturity)

for a certain price F (forward price , de-livery price)

- The party who agrees to buy the asset

is said to have a long position ; the party

who agrees to deliver the asset is said to

have the short position.

- If the forward price is chosen carefully,

then the contract has no value initially,

i.e. it costs nothing for either party

to enter into the contract. The con-

tract value changes in time depending onconditions in the market.

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If the spot price of the asset at time T

is S(T) then the party in the long posi-

tion has agreed to pay (and the party in

the short position has agreed to accept)

a price F for what is worth S(T). The

payoff to the holder is therefore

S(T) F,

which may be positive or negative; simi-

larly, the payoff to the seller is

F S(T).

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Payoffs cancel out: one partys gain is the

other partys loss

Forwards are a zero-sum game.

[ see payoff diagram ]

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A futures contract is very similar to a

forward contract. However, interim prof-its and losses are paid throughout the life

of the contract rather than just at matu-

rity.

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Example - agriculture forwards: Mrs

Mkhize is a farmer in Northern Kwa-Zulu

Natal and one of her specialities is pota-toes. She knows that her potatoes will

be ready for sale and delivery in three

months time. Due to the good rains

during the season, she expects to har-

vest three tons of potatoes. She also

knows that the harvest countrywide will

be a good one and is worried that she

wont be able to sell all her potatoes, or

that she will be forced to sell them at a

discounted price and suffer a loss.

The Roar Food Company in Johannes-

burg produces potato chips. The com-

pany expects an influx of tourists to South

Africa due to a reduction in the currency

and the sporting events taking place dur-

ing the summer. The company has bud-geted a huge increase in production in

three months time, and is scared that

there will not be sufficient potatoes avail-

able in the market, or that the demand

would increase, thus pushing up prices.

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Mrs Mkhize and the Roar Food Company

close a contract whereby Mrs Mkhize un-

dertakes to supply the company with threetons of potatoes in three months time.

The Roar Food company undertakes to

buy three tons of potatoes from Mrs Mkhize

at R1 000 per ton on delivery of the pota-

toes. The market price of potatoes at the

closing of the contract is R950 per ton.

Both parties are using the forward con-

tract, a derivative as a hedging tool.

The market price of potatoes at the clos-

ing of the contract has no direct effecton the contract except that it acts as a

guideline to the determination of the con-

tract price (R1000).

At the date of delivery determined in the

contract (called the close-out date), MrsMkhize has an obligation to supply three

tons of potatoes and the Roar Food Com-

pany has an obligation to take delivery of

the potatoes and pay Mrs Mkhize R3000

(R1 000 x 3).

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If the market price of potatoes on the day

of delivery (the close-out day of the con-

tract) is R1050, then Mrs Mkhize could

have sold her potatoes in the market atR1 050 (assuming the demand is high

enough). She loses while Roar gains. On

the other hand, if market price drops to

R850, then she saves R450 through the

contract while Roar forks out the sameamount extra for the hedge.

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Example - Forex forwards: A local Biotech

company knows that it will need to buy

equipment to the value of Eu. 1 million

from a German manufacturer in 3 months

time.

To hedge against forex risk, the company

looks into the possibility a forward con-

tract with a suitable bank (an SA Re-

serve Bank approved forex dealer) . The

following ZAR/Euro exchange rates are

quoted:

Bid Offer

Spot 7.1789 7.20090-day forward 7.2590 7.2622

There are two options for the company

enter forward contract to buy Euros at

7.2622 ZAR per Euro

or

buy Euros at the prevailing rate in 3

months time

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How are forward rates calculated?

The bank determines the forward rate in

the contract in the following manner:

The bank takes on the foreign exchange

exposure and has to cover this risk. It

must have 1 million Euros in three months

time to give to the company. It is an ap-

proved forex dealer, so the bank can buyEuros now and place it on deposit in a

German bank, to ensure that it has the

right amount in three months time.

The bank, however, does not have to buy

the full amount now, as it will receive in-

terest (say the European deposit rate is

4%) for the three months on the deposit

at the US bank. The bank therefore only

buys:

1000000

1 + (i t/365)

where

i denotes short-term deposit rate in the

European Union and t denotes the term

of deposit.

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The bank thus buys:1000000

1 + ( 0.04 91/365)= 990 126.87

To buy 990 126.87 Euros now, the bank

must pay rand at the current exchange

rate - the bank thus pays:

990 126.87 7.2 = R7128913.46.

The bank must borrow this ZAR amount

to purchase Euros at the current short-

term interest rate in SA for 3 months (or

at the cost of capital of the bank if it uses

internal funds). If the current short-term

rate in SA is 7.5%, the bank will have to

pay:

R7128913.46 7.5%

91

365 = R133 300.92interest to its lender in 3 months time.

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This interest paid by the bank will be

borne by the company and will be dis-

counted in the forward rate. The total

cost to the bank for this transaction is

thus:

The cost of the Euro loan R7128913.46

plus the interest on the loan R133 300.92,

i.e. R7262214.38.

The forward rate is then calculated by the

total cost divided by the amount in Euros:

R7262214.38

1000000 R7.2622.

This gives 3 month forward rate.

30 and 60 day forward rates can be ob-tained similarly.

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2.2: Options

An european call option gives the holder

the right to buy an asset S (the underly-

ing) for an agreed amount K (the strike or

exercise price) on a specified future dateT (the maturity or expiry date).

- The party who undertakes to deliver the

asset is called the writer of the option.

- The holder of the option does not have

to exercise the option. Hence, the payoff

to the holder is never negative (ignoring

the cost of the contract). Thus the pay-

off is

max{S(T)K, 0}.

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[ insert payoff diagram for call option]

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Since the payoff is never negative, the

contract comes with a price ! i.e. op-

tion contracts, unlike forwards, have a

price associated with them.

The purchaser (holder) pays the writer a

premium up front to enter into the con-

tract.

For a call option the option price repre-

sents a premium paid for the risk that the

spot price of the underlying will rise above

the agreed upon strike price at maturity.

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[ insert profit diagram for call option]

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A european put option gives the holder

the right to sell an asset at a future date

at an agreed upon price.

An american call (put) option gives theholder the right to buy (sell) an asset

for an agreed amount. However, the op-

tion can be exercised at any time, not

just at maturity.

An option expires out of the money if

- S(T) < K for a call and

- S(T) > K for a put option.

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[ insert payoff and profit diagrams for putoption]

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The buyer of an option stands to lose at

most the premium paid up front. This

happens if the option expires out of the

money and option is not exercised.

Comment: a forward contract can be con-

structed using options. A forward con-

tract with delivery price K and expiry T

is equivalent to a portfolio which is long a

call option and short a put option which

both have strike price K and expiry T.

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Using options to hedge:

An investor owns 1000 shares of ABC,

valued at R100 per share. If the share

price drops to R90 in the next quarter

the investor will suffer a loss of R10 000.

To hedge against this risk, the investor

purchase a put option to sell 1000 shares

at R95 per share in 4 months time.

Now if the price drops to R90 per share,

the loss thus becomes limited to R5 000

plus the premium for the put.

If the price rises instead to R104 per share,

then the investor gains R4 000 minus the

premium of the put.

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Using options for leverage:

Joe believes strongly that the shares of

firm GenX, which manufactures power gen-

erators, will rise rapidly in the next quar-

ter. He is willing to speculate R10 000 on

this view.

GenX shares are currently trading at R50

per share, so Joe could buy 200 shares.

If the share price rises to R60 in 4 monthstime, then Joe will make a profit of R2 000.

If the price drops to R40 per share, then

he will lose R2 000.

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Joe decides instead to buy call options.

Call options to buy 100 GenX shares, strik-

ing at R53, maturing in 4 months time

and which are priced at R200 are avail-

able. Joe can buy 50 of these with his

R10 000; he will be able to purchase 5 000

shares if the options mature in the money.

If the share price rises to R60, then Joe

will make a profit of

5000 (60 53)R10 000 = R25 000.

If the share price drops below R53, then

he loses his entire R10 000.

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Derivative Markets (international, 2002)

DERIVATIVE TYPES amounts(billions of US$)

OTC contracts: 270 100

1. FOREX contracts 31 075Forwards & forex swaps 16 031Currency swaps 8 236Options 6 809

2. Interest rate contracts 204 393FRAs 13 573Interest rate swaps 163 749Options 27 071

3. Equity-linked contracts 5 145Forwards and swap 1 176Options 3 968

4. Commodity contracts 1 693Gold 288Other commodities 1 406

5. Other OTC contracts 27 793

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DERIVATIVE TYPES amounts(billions of US$)

Exchange traded 58 281.4

contracts:

1. Futures 20 696.9Interest rate 19 860.3Currency 109.7Equity index 726.8

2. Options 37 584.5Interest rate 32 794.9Currency 63.1Equity index 4 726.5

TOTAL 328 381.4

http://www.bis.org/publ/quarterly.htm

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Myths, legends and tales of woe ...

Famous case studies:

* LTCM,

* Metallgesellschaft,

* Barings (Nick Leeson - Rogue trader).

http://www.erisk.com/Learning/CaseStudies.asphttp://www.erisk.com/Learning/CaseStudies/

WheelofMisfortune.asp

BOOKS:

Inventing money by Nicholas Dunbar (LTCM

- more math),

When Genius Failedby Roger Lowenstein (LTCM

- more people),

Fooled by Randomnessby Nassim Taleb (gen-

eral)

Liars Poker by Michael Lewis (bond trading

and Wall Street in the 80s)

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SOME Look-up LINKS:

http://www.riskglossary.com

http://www.optionsxpress.com/

http://www.investopedia.com/

http://www.investorwords.com/

http://global-derivatives.com/maths/a-e.php

http://global-derivatives.com/options/o-types.ph

http://www.wikipedia.org/

http://www.in-the-money.com/glossarynet/keyind

Documents

FIRM06_Ch1and2