A&J Flashcards for exam SOA Exam FM/ CAS Exam 2

A&J Flashcards for

Exam FM/2 Spring 2010

Alvin Soh

Outline

I. Theory of Interest A) Measurement of Interest B) Valuation of Annuities C) Yield Rates D) Amortization and Sinking Funds E) Pricing Common Stocks F) Bonds G) Advanced Financial Analysis

II. Derivatives Markets A) Introduction to Derivatives and Risk B) Forward Contract C) Options D) Contracts and Positions E) Insurance and other Option Strategies F) Risk Management G) Financial Forwards and Futures H) Swap

Theory of Interest- Measurement of Interest

Accumulation Function

Theory of Interest- Measurement of Interest

( ) 1 1a t a t i or ( ) 1 1A t A t i

where

,A t ka t k is the principal .

Theory of Interest- Measurement of Interest

Effective Rate of interest for period 1t to t

Theory of Interest- Measurement of Interest

( ) ( 1)

( 1)

a t a ti

a t

Theory of Interest- Measurement of Interest

The accumulation function for simple interest.

Theory of Interest- Measurement of Interest

1a t it

Theory of Interest- Measurement of Interest

Effective rate of interest for Simple Interest from period 1t to t

Theory of Interest- Measurement of Interest

( ) ( 1) (1 ) (1 ( 1))

( 1) 1 ( 1) 1 ( 1)t

a t a t it i t ii

a t i t i t

This is the reason that the effective rate of interest is decreasing as the time

of accumulation increases.

Theory of Interest- Advanced Financial Analysis

The relationship between spot rate and forward rate.

Theory of Interest- Advanced Financial Analysis

where

1. ts is the spot rate at at time t ;

2. tf is the t –year forward rate.

1 2

1 1 2 2 1

1 1 2 1

1

1 1 1 1 1

1 1 ... 1 1

t

t

t t

t t t t t

t t

s

s f s f f

s f f f

Theory of Interest- Advanced Financial Analysis

The real interest rate after inflation

Theory of Interest- Advanced Financial Analysis

11 '

1

ii

r

where

1. i is the nominal interest rate; 2. r is the inflation rate.

Theory of Interest- Advanced Financial Analysis

Macaulay Duration

Theory of Interest- Advanced Financial Analysis

1

1

nt

t

t

nt

t

t

tv CF

d

v CF

Theory of Interest- Advanced Financial Analysis

Modified Duration

Theory of Interest- Advanced Financial Analysis

1

1 1 1

1 1 1

n n nt t t

t t t

t t t

n n nt t t

t t t

t t t

dd v CF tv CF tv CFPdidiv v vd

Pv CF v CF v CF

Theory of Interest- Advanced Financial Analysis

Convexity

Theory of Interest- Advanced Financial Analysis

2

1 2

21 1

1 1

1n n

t t

t t

t t

n nt t

t t

t t

dd tv CF t t v CFPdidic

Pv CF v CF

Theory of Interest- Advanced Financial Analysis

The conditions for Redington Immunization

Theory of Interest- Advanced Financial Analysis

1.

2. OR

3.

Assets Liabilities

Assets Liabilities Assets Liabilities

Assets Liabilities

P i P i

d i d i v i v i

c i c i

Derivatives Markets- Introductions

The purposes of Derivatives

Derivatives Markets- Introductions

1. Speculation 2. Portfolio Replication 3. Arbitrage 4. Risk Management

Derivatives Markets- Introductions

Buying Price by end users =

Selling Price by end users =

Derivatives Markets- Introductions

Buying Price by end users = Ask Price

Selling Price by end users = Bid Price

(Bank Buy : Bid Price)

Derivatives Markets- Contracts and Positions

The meaning of Long and Short positions

Derivatives Markets- Contracts and Positions

Long position When a trader buys an option contract that he has not already

written (i.e. sold), he is said to be opening a long position. When a trader sells an option contract that he already owns, he is

said to be closing a long position. When a trader is 'long', he/she wins when the price increases, and

loses when the price decreases. Short position

When a trader writes (i.e. sells) an option contract that he does not already own, he is said to be opening a short position.

When a trader buys an option contract that he has written (i.e. sold), he is said to be closing a short position.

When a trader is 'short', he/she wins when the price decreases, and loses when the price increases.

Derivatives Markets- Contracts and Positions

Long positions using forward contract, call option and put option

Derivatives Markets- Contracts and Positions

1. Long forward contract 2. Purchased call 3. Written put

Derivatives Markets- Contracts and Positions

The profit of written put

Derivatives Markets- Contracts and Positions

max 0,rT

TWritten Put Profit Pe K S

Written Put Profit vs. Asset Price

Profit

Asset Price 0

K K-FV(P)

-(K- FV(P))

FV(P)

Derivatives Markets- Contracts and Positions

Short positions using forward contract, call option and put option

Derivatives Markets- Contracts and Positions

1. Short forward contract 2. Purchased put 3. Written call

Derivatives Markets- Contracts and Positions

The profit of written call

Derivatives Markets- Contracts and Positions

max 0,rT

TWritten Call Profit Ce S K

Written Call Profit vs. Asset Price

Profit

Asset Price 0 K

K+FV(C)

FV(C)

Derivatives Markets- Contracts and Positions

Comparisons of long positions using forward contract, call option and put option in terms of:

1. Maximum loss 2. Maximum profit 3. Range of underlying asset price such that the profit is positive

Derivatives Markets- Contracts and Positions

Method Maximum Loss Maximum Profit Positive Profit

Long forward Forward Price Unlimited ST > F

Purchased Call Future value of call premium

Unlimited ST > K+FV(C)

Written Put K – FV(P) Future value of put premium

ST > K-FV(P)