Lecture No.1 By M Fahad Siddiqi Lecture (Finance) IBMS
Dec 26, 2015
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?
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