Salaar - FinanceINVESTMENTS BBA SUMMER Semester 2010 Lahore School of Economics Salaar farooq – Assistant Professor

Salaar - Finance RISK & RETURN of Investing

Salaar - Finance Returns & Risks from Investing Learning Objectives What is return? What is risk? Sources of risk? Types of risk? How to measure risk? How to measure returns? Realized returns & risks from investing Practice Problems

Salaar - Finance Returns Objective of Investors ?

Salaar - Finance Returns Objective of Investors To maximize expected returns Constraint: risk

Salaar - Finance Returns Components of investment returns ?

Salaar - Finance Returns Components of investment returns Yield Income component of a security’s return from cash flows Relates the C/F’s to the price of the security Capital gain (loss) Change in price of a security over time

Salaar - Finance Returns Components of investment returns Total Return = Yield + Price Change (CG) Yield can be 0 or + CG can be 0,+ or -

Salaar - Finance Returns Examples of components A Bond purchased at par held to maturity: ? A Bond purchased for $800 & held till maturity? A non-dividend stock? A dividend paying stock?

Salaar - Finance Returns Examples of components A Bond purchased at par held to maturity: ? Yield only A Bond purchased for $800 & held till maturity? Y+PG A non-dividend stock? PG only A dividend paying stock? Y+PG

Salaar - Finance What is Risk?

Salaar - Finance What is Risk? UNCERTAINTY OF FUTURE OUTCOMES Definition of Risk: Risk is the Probability… ACTUAL OUTCOME will be different from EXPECTED OUTCOME. Which outcome are we discussing? Future Returns

Salaar - Finance   Future Decision Expected Outcome 1,2…n (return) RISK of deviation Risk Calculation is on Historical Data T=0 T=-n Risk exposure involves Future time

Salaar - Finance What are the Sources of Risk? An Overview –Price risk –Interest Rate risk –Market risk –Inflation risk –Business risk

Salaar - Finance What are the Sources of Risk? An Overview –Price risk Variability in security’s returns due to price fluctuations –Interest Rate risk Variability in ER due to changes in interest rates –Market risk Variability in ER due to changes in overall market –Inflation risk Variability in ER due to changes in purchasing power (interest rates) –Business risk Variability in ER due to exposure to a particular industry

Salaar - Finance What are the Sources of Risk? An Overview –Financial risk –Liquidity risk –Exchange rate risk –Country risk (political risk)

Salaar - Finance What are the Sources of Risk? An Overview –Financial risk Arises due to debt financing. Variability in ER due to leverage –Liquidity risk Variability in ER due to inability to trade in secondary mkts. time & price concession required to sell securities –Exchange rate risk Variability in ER due to currency fluctuations. –Country risk (political risk) Variability in ER due to instability of the political system.

Salaar - Finance What are the Sources of Risk? Summary –Price risk –Interest Rate risk (affects market value & resale price) –Market risk (overall market effects) –Inflation risk (purchasing power variability) –Business risk (unique risk) –Financial risk (tied to debt financing) –Liquidity risk (time & price concession to sell securities) –Exchange rate risk (fx) –Country risk (political risk)

Salaar - Finance What Types of Risk are there?

Salaar - Finance What Types of Risk are there? –2 Main Types –Systematic risk: (MKT) also called market risk or non-diversifiable risk. Caused by the market as a whole –Non-Systematic risk: (COMPANY) also called non-market risk or diversifiable risk. This risk is caused by factors unique to the company

Salaar - Finance Types of Risk Average annual standard deviation (%) Number of stocks in portfolio Diversifiable risk (unique risk) Non-diversifiable risk (market risk)

Salaar - Finance How do we measure Risk? Probability distributions Probability distributions combine outcomes to probabilities Multiply possible returns by associated probabilities and sum them The probabilities must sum to 1.0

Salaar - Finance Prob. Returns

Salaar - Finance How do we measure Risk? The risk for a security can be calculated using Standard Deviation measure

Salaar - Finance Variance of return where N is the number of returns Standard deviation of return

Salaar - Finance How do we use information regarding risk? Analytical Development In Finance, decision rules are based on benchmark or alternative comparisons. E.g. consider the statement: A: an investment (IND: X) has an ER of 35% with SD of 30%

Salaar - Finance How do we use this information regarding risk? Analytical Development In Finance, decision rules are based on benchmark or alternative comparisons. E.g. consider the statement: A: an investment (IND: X) has an ER of 35% with SD of 30% B: an investment (IND: X) has an ER of 35% with SD of 15%

Salaar - Finance How do we use this information regarding risk? Analytical Development In Finance, decision rules are based on benchmark or alternative comparisons. E.g. consider the statement: A: an investment (IND: X) has an ER of 35% with std dev of 30% B: an investment (IND: X) has an ER of 35% with std dev of 15% C: IND X has an industry AR of 50% with std dev of 15%. Given the alternatives, & ATE both A & B are inferior. Therefore, one question you must always ask regarding risk is “what are the alternatives or benchmarks to compare with?” M-10

Salaar - Finance SUMMARY STATISTICS FOR RETURNS Arithmetic mean : The mean return Geometric mean Compounded rate of return over time – r at which end value is obtained. G = (1+TR)^(1/n) – 1 1+TR = RR is used since –ve TR’s cannot be used for G

Salaar - Finance SUMMARY STATISTICS FOR RETURNS Arithmetic mean vs geometric mean When should you use the AM or GM? AM: A)better measure of average performance over single periods. B)Best estimate of ER for next period GM: a)better measure of the change in wealth over multiple periods

Salaar - Finance Risk Premiums Risk Premium Equity Risk Premium

Salaar - Finance Risk Premiums Risk Premium Additional Compensation for assuming risk Equity Risk Premium Difference between return on stocks & the risk-free rate (t-bills)

Salaar - Finance Risk Premiums Equity Risk Premium ERP = ( (1+TR stock) / (1+Rf) ) – 1 M 6

Salaar - Finance PROBLEM # 9Calculating ERP Common stocks had a return of % over 80yrs. T- bills had a return of % over the same period. a)What is the historical Equity Risk Premium?

Salaar - Finance PROBLEM # 9Calculating ERP Common stocks had a return of % over 80yrs. T-bills had a return of % over the same period. a)What is the historical Equity Risk Premium? ERP = / – 1 =.0578 = 5.78%

Salaar - Finance Part II

Salaar - Finance MEASURING RETURNS TOTAL RETURN Total return (TR) A %age relating ALL C/F’s received by an investor to the purchase price during a period.

Salaar - Finance MEASURING RETURNS TR FORMULA Total return (TR) TR = (All C/F’s + Price Changes) / purchase Px. Or TR = C + (P.e – P.b) / Pb E = end period b= beginning period

Salaar - Finance MEASURING RETURNS Advantages of TR Gives a measure of return in % Allows comparison b/w different assets Includes realized & unrealized gains

Salaar - Finance PROBLEM # 1Example TR Suppose you purchase a 10% coupon Bond at $960. After a year you sell it for $1020. a)What is the TR?

Salaar - Finance PROBLEM # 1Example TR Suppose you purchase a 10% coupon Bond at $960. After a year you sell it for $1020. a)What is the TR? TR = 100+( ) / 960 = / 960 = or 16.67%

Salaar - Finance PROBLEM # 2Example TR Suppose you purchase 100 shares of JNJ at $30 per share. After a year you sell for $26. A dividend of $2 is paid during the year. a)What is the TR?

Salaar - Finance PROBLEM # 2Example TR Suppose you purchase 100 shares of JNJ at $30 per share. After a year you sell for $26. A dividend of $2 is paid during the year. a)What is the TR? 2 + (26-30) / 30 = 2 + (-4) / 30 = = (6.67%)

Salaar - Finance MEASURING RETURNS RETURN RELATIVE Return Relative (RR) Total return of an investment for a given period expressed on a base of 1.0 Why To calculate cumulative wealth index OR geometric means which cannot use –ve returns

Salaar - Finance MEASURING RETURNS Return Relative - Formula RR RR = TR in decimal Therefore, TR in decimal = RR – 1.0 Since its expressed as 1 base, modified TR RR = (C+ Pe) / Pb

Salaar - Finance PROBLEM # 3Example RR If the TR is 10%, & -9.07% then, a)What is the RR?

Salaar - Finance PROBLEM # 3Example RR If the TR is 10%, & -9.07% then, a)What is the RR? 10% TR,RR = TR + 1 = = % TR, RR = TR + 1 = =

Salaar - Finance PROBLEM # 4Example RR If the Dividend is & the security price is One year earlier it was , a)What is the RR?

Salaar - Finance PROBLEM # 4Example RR If the Dividend is & the security price is One year earlier it was , a)What is the RR? RR = ( – ) / =

Salaar - Finance MEASURING RETURNS Cumulative Wealth Index CWI Cumulative wealth over time, given an initial wealth & a series of returns on an asset. WHY? TR tracks changes in wealth, CWI measures LEVELS of wealth, rather than changes. Measures the effect of returns on the wealth. Uses $1 as the beginning base amount for convenience.

Salaar - Finance MEASURING RETURNS CWI - Formula CWI CWI = WI.(1+TR1).((1+TR2) … n where, CWI = end of period wealth WI = beginning index value usually 1 TRn = Periodic TR’s in decimal form

Salaar - Finance PROBLEM # 5Example of CWI The values of the S&P were as follows: 1990 = & TR= -3.14% 1991 = = 30% 1992 = = 7.43% 1993 = = 9.94% a)What are the Return Relatives? b)What is the CWI?

Salaar - Finance PROBLEM # 5Example of CWI The values of the S&P were as follows: 1990 = & TR = -3.14% 1991 = = 30% 1992 = = 7.43% 1993 = = 9.94% a)What are the Return Relatives? RR’s = =0.969, 0.3+1=1.3, =1.0743, = b)What is the CWI? 1(.969)(1.3)(1.0743)(1.0994) =

Salaar - Finance MEASURING RETURNS CWI - NOTE Calculating TR’s from CWI TRn = (CWI n / CWI n-1) – 1 TRn = total return for period n CWI = cumulative wealth index at n TRn = Periodic TR’s in decimal form

Salaar - Finance PROBLEM # 6Getting TR from CWI Suppose CWI,2005 = & CWI,2006 = , a)what’s the TR?

Salaar - Finance PROBLEM # 6Getting TR from CWI Suppose CWI, 2005 = & CWI, 2006 = , a)what’s the TR? / – 1 = – 1 = 73.32% M11

Salaar - Finance TAKING A GLOBAL PERSPECTIVE Investing Internationally Exchange rate risk? Calculating TR for foreign positions NOTE: Foreign currency is stated in domestic terms

Salaar - Finance MEASURING RETURNS Formula – Fx Positions TR TR return in domestic terms TRd = (RR x Ending Value Fx/Begin Value Fx) -1 TRd = total return in domestic terms

Salaar - Finance PROBLEM # 8FX returns Suppose you are in Pk & invest in Walmart at $ 50 when the value of 1 dollar in Rs. is 60. One year later, Walmart is $55 & there is no dividend. The dollar is now Rs. 57, which means the Rs appreciated against the dollar. a)Calculate the RR for Walmart? b)What is your TR in Rs after currency adjustment?

Salaar - Finance PROBLEM # 8FX returns Suppose you are in Pk & invest in Walmart at $ 50 when the value of 1 dollar in Rs. is 60. One year later, Walmart is $55 & there is no dividend. The dollar is now Rs. 57, which means the Rs appreciated against the dollar. a)Calculate the RR for Walmart? RR = 55/50 = 1.10 b)What is your TR in Rs(domestic) after currency adjustment? 1.1 x (57/60) – 1 = 1.1*.95 = – 1 =.045 = 4.5%.

Salaar - Finance Some Realities of risk in the real world Realized Returns Over Long Periods ( ) Some benchmarks for Returns & Risks on major assets over long periods: –Common stocks--approx 13% std dev 20% (more risky) –AAA corporates—approx 6% std dev 9% –Treasury bonds—approx 5.4% std dev 8% –T-bills— approx 4% std dev 3%

Salaar - Finance Summary We have learnt the following about Risk: What is Risk? Uncertainty about future outcomes How do we define it? The chance of Actual VS Expected How do we measure it? Standard Deviation How do we use this information to make financial decisions? (benchmarks) What are the sources of risk? Price,market,interest rate, etc How many types of risk are there? Unique & Market What are benchmark Realities of Risk? Stocks, Bonds, T-bills

Salaar - Finance END