Lecture No.1

By M Fahad SiddiqiLecture (Finance)IBMS

What is investmentAn asset or item that is purchased with the hope that it will generate income or appreciate in the future. In an economic sense, an investment is the purchase of goods that are not consumed today but are used in the future to create wealth. In finance, an investment is a monetary asset purchased with the idea that the asset will provide income in the future or appreciate and be sold at a higher price.

Objective of investment Investment is a conscious act of an

individual or any entity that involves deployment of money (cash) in securities or assets issued by any financial institution with a view to obtain the target returns over a specified period of time.

Target returns on an investment include:1. Increase in the value of the securities or

asset, and/or2. Regular income must be available from

the securities or asset.

Definition of Investment Specifically, an investment is the

current commitment of dollars for a period of time in order to derive future payments that will compensate the investor for

(1) the time the funds are committed, (2) the expected rate of inflation, and (3) the uncertainty of the future payments (Frank Reilly and Keith Brown)

Issues with investment

1. The Time The Funds Are CommittedIn other words it is sacrifice like in investing, the investor delay their current consumption (delaying consumption is kind of sacrifice) 2. The expected rate of inflationInvestment loses value in periods of inflation (3) the uncertainty of the future payments

giving your money to someone else involves risk

ReturnsIf you buy an asset of any type,

your gain (or loss) from that investment is called the return on your investment.

Return will usually have two components. First, you may receive some cash directly while you own the investment.

Second, the value of the asset you purchase may change.

Example

Case1 Case2

Ending Stock Prices 69.96 39.78

Jan 1st value 5000 5000

Dec 31 value 6996 3978

Dividend Income 81 81

Capital Gain or Loss 1,996 ?

suppose you purchased 100 shares of stock in Harley-Davidson on January 1. At that time, Harley was selling for $50 per share, so your 100 shares cost you $5,000. At the end of the year, you want to see how you did with your Investment ?

Dividend income At the beginning of the year, on

January 1, the stock is selling for 50 per share, and,

as we calculated above, your total outlay for 100 shares is 5,000. Over the year, Harley pays dividends of $.81 per share. So Your dividend income is

Dividend income = .81 * 100 =$81

Capital GainIn Case 1. December 31, Harley

was selling for $69.96, meaning that the value of your stock increased by $19.96 per share. Your 100 shares are now worth $6,996,

so you have a capital gain ofCapital gain = ($69.96 - $50) *

100 =$1,996. Can you tell the capital gain/loss

in case 2

PERCENTAGE RETURNS  Case 1 Case 2

January 1 stock Prices, Pt

50.00 50.00

Dec 31st stock Prices, Pt+1

$69.96 $39.78

Dividend Income, Dt+1

.81 .81

Capital Gain or losses

19.96 10.22

dividend yield: The annual stock dividend as a percentage of the initial stock prices.Dividend yield = Dt+1 / Pt

=$.81 / $50 = 0.0162 = 1.62%

PERCENTAGE RETURNScapital gains yield The change in stock price as a

percentage of the initial stock Price

capital gains yield = (Pt+1 - Pt )/Pt

=($69.96 -$50) / $50 =$19.96/$50 = .3992 = 39.92%

PERCENTAGE RETURNSTotal Percent Return: The return

on an investment measured as a percentage that

accounts for all cash flows and capital gains or losses.Percentage return =Dividend yield +Capital gains yieldPercentage return = Dt+1 / Pt + (Pt+1 -

Pt )/Pt

= (Dt+1 + Pt+1 - Pt ) / Pt

ANNUALIZING RETURNSeffective annual return (EAR)The return on an investment

expressed on a per-year, or “annualized,” basis

For example, suppose you bought 200 shares of XYZ at a price of $48 per share. In three months, you sell your stock for $51. You didn’t receive any dividends. What is your return for the three months? What is your annualized return?.

Return when no Dividendcapital gains yield = (Pt+1 - Pt )/Pt

= (51-48)/48 = .0625 = 6.2%

effective annual return (EAR)=1 + EAR = (1 + holding period percentage return)m

where m is the number of holding periods in a year. = (12/3) = 4 1+ EAR= (1 +.0625) 4

=1.2744So, your annualized return is 27.44

percent.

QUESTIONS 1Suppose you buy some stock in

Qwest (no, that’s not a typo, that’s how the company spells it) at a price of $8 per share. Four months later, you sell it for $8.40. No dividend is paid. What is your annualized return on this investment?

QUESTION 2Suppose you buy some stock in

Johnson & Johnson (JNJ) at a price of $50 per

share. Three years later, you sell it for $62.50. No dividends were paid. What is your annualized return on this investment?

Lets Play with DataAnd find pattern in Historical

returns in Pakistani Stock Market.

10-18

Arithmetic vs. Geometric Mean

Arithmetic average: ◦ Return earned in an average period over

multiple periods◦ Answers the question: “What was your return

in an average year over a particular period?”Geometric average:

◦ Average compound return per period over multiple periods

◦ Answers the question: “What was your average compound return per year over a particular period?”

Geometric average < arithmetic average unless all the returns are equal

10-19

Geometric Average Return: Formula

1R1(...)R1()R1(GAR /T1N)21

Where:

Ri = return in each period

T = number of periods

Equation 10.4

10-20

Geometric Average Return

1)R1(GART/1T

1ii

Where:

Π = Product (like Σ for sum)

T = Number of periods in sample

Ri = Actual return in each period

10-21

Example: Calculating a Geometric Average ReturnExample 10.4

Percent One Plus CompoundedYear Return Return Return:1926 11.14 1.1114 1.11141927 37.13 1.3713 1.52411928 43.31 1.4331 2.18411929 -8.91 0.9109 1.98951930 -25.26 0.7474 1.4870

1.0826

8.26%

(1.4870)^(1/5):

Geometric Average Return:

10-22

Arithmetic vs. Geometric MeanWhich is better?

The arithmetic average is overly optimistic for long horizons

The geometric average is overly pessimistic for short horizons

Depends on the planning period under consideration• 15 – 20 years or less: use arithmetic• 20 – 40 years or so: split the difference between

them• 40 + years: use the geometric