BSC/BBA III Summer Semester 2010 Lahore School of Economics

Chap 06 Risks & Returns from Investing

Risk and Return Overview & Background Investing involves decisions for the future Key variable with future = Uncertainty Expected Returns is basis of Investments Biggest Threat: UNCERTAINTY = RISK Uncertainty represents RISK conceptually Investors must estimate & manage Risk Risk & Return are opposite sides of the same coin R&R involve a trade-off with each other

Returns Objective of Investors ?

Returns Objective of Investors To maximize expected returns Constraint: risk

Returns Components of investment returns ?

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

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

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?

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

What is Risk?

UNCERTAINTY OF FUTURE OUTCOMES Definition of Risk: Risk is the Probability (chance) the ACTUAL OUTCOME will be different from the EXPECTED OUTCOME. Which outcome are we discussing? Specifically, investors are worried the actual outcome (of returns from their investments) will be less than the expected returns.

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

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

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 Business risk Variability in ER due to exposure to a particular industry

What are the Sources of Risk? An Overview Liquidity risk Variability in ER due to inability to trade in secondary markets. 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.

Financial Risk Effects of Financial Leverage?.. Financial Leverage refers to the extent to which a firm relies on Debt. More Debt means MORE leverage The larger the proportion of assets financed by debt, the larger the variability in returns, other things being equal.

Financial Risk - Example We consider case of company X which has no debt & is considering restructuring to include debt in its capital structure. We look at DEBT & NO DEBT situations Taxes are ignored

Financial Risk - Example CurrentProposed Assets$8,000,000 Debt04,000,000 Equity8,000,0004,000,000 Debt-Equity Ratio 01 Share Price20 # of Shares400,000200,000 Interest Rate10%

Financial Risk - Example Current Capital Structure: No Debt RecessionNormalExpansion EBIT$500,000$1,000,000$1,500,000 Interest??? Net Income??? ROE??? EPS???

Financial Risk - Example Current Capital Structure: No Debt RecessionNormalExpansion EBIT$500,000$1,000,000$1,500,000 Interest 000 Net Income 500,0001,000,0001,500,000 ROE 6.25%12.5%18.75% EPS

Financial Risk - Example Proposed Capital Structure: Debt - $4 Million RecessionNormalExpansion EBIT$500,000$1,000,000$1,500,000 Interest??? Net Income??? ROE??? EPS???

Financial Risk - Example Proposed Capital Structure: Debt - $4 Million RecessionNormalExpansion EBIT$500,000$1,000,000$1,500,000 Interest 400,000 Net Income 100,000600,0001,100,000 ROE 2.50%15.50%27.50% EPS

MEASURING RETURNS Total return Return relative Cumulative wealth index Inflation adjusted returns

TOTAL RETURN The Total Return for a given time period is a decimal number (or a percentage) relating all the cash flows received by an investor during designated time period to the purchase price of the Asset. TR = Any Cash Payment Received + Price change over time period Price at which the Asset is Purchased Or TR = CF t + (P.e – P.b) = CF T + PC P B P B

Total Return - Advantages 1.It is all inclusive 2.Allows comparison b/w different assets 3.Includes realized & unrealized gains

Suppose you purchase a 10% coupon Bond at $960. After a year you sell it for $1020. What is the TR? Total Return - Example

Suppose you purchase a 10% coupon Bond at $960. After a year you sell it for $1020. What is the Total Return? TR = {100 + ( )} / 960 = { }/ 960 = or 16.67% Total Return - Example

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. What is the TR?

Total Return - Example 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. What is the TR? TR= {2 + (26-30)}/ 30 = {2 + (-4)} / 30 = or (6.67%)

RETURN RELATIVE 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, both of which cannot use negative returns. RR = TR in decimal = {C + P E }/P B Or, TR= RR – 1.0

RETURN RELATIVE - Example If the TR is 10% & -9.07% then, What is the RR?

RETURN RELATIVE - Example If the TR is 10% & -9.07% then, What is the RR? CASE 1:TR = 10% RR = TR + 1 = = 1.1 Case 2:TR= -9.07% RR = TR + 1 = =

RETURN RELATIVE - Example If Dividend paid is & the security price is One year earlier it was , What is the RR?

RETURN RELATIVE - Example If Dividend paid is & the security price is One year earlier it was , What is the RR? RR = ( ) / =

Cumulative Wealth Index Cumulative wealth index measures the cumulative effect of returns over time, given some stated beginning dollar amount invested, which typically is shown as $1 for convenience. WHY? TR tracks changes in wealth, CWI measures LEVELS of wealth, rather than changes. Measures ending wealth (cumulative wealth) over some period on the base of beginning $ 1.

Cumulative Wealth Index CWI = WI 0 (1+TR 1 )(1+TR 2 ) … (1 + TR N ) where, CWI = end of period wealth WI 0 = beginning index value usually $1 TR N = Periodic TR’s in decimal form

Cumulative Wealth Index - Example Values & Total Returns for S&P500 for past few years were as follows: ValuesTotal Return 1990: % 1991: % 1992: % 1993: % What is the CWI?

Cumulative Wealth Index - Example Values & Total Returns for S&P500 for past few years were as follows: ValuesTotal Return 1990: % 1991: % 1992: % 1993: % What is the CWI? CWI= 1(.969)(1.3)(1.0743)(1.0994) =

Cumulative Wealth & Total return TR N = (CWI N / CWI N-1 ) – 1 Where, TR N = Total Return for period N CWI N-1 = Cumulative Wealth Index at period N - 1 CWI N = Cumulative Wealth Index at period N

Cumulative Wealth & Total return - Example Suppose CWI in 2005 = & CWI in 2006 = , what’s the TR in year 2006?

Cumulative Wealth & Total return - Example Suppose CWI in 2005 = & CWI in 2006 = , what’s the TR in year 2006? TR 2006 = (2.5787/1.4878) – 1 = – 1 = 73.32%

International Returns & Currency Risk Currency Risk is the Risk that the change in the value of the domestic & the foreign Currency involved will be unfavorable. When investors buy & sell assets in other countries, they must consider exchange rate or Currency Risk. Why?

International Returns & Currency Risk When investors buy & sell assets in other countries, they must consider exchange rate or Currency Risk. Why? When investors invest in Assets denominated in Foreign currency, they are actually investing in two Assets: 1. Financial security in Foreign Country 2. Foreign Currency Thus, They need to be concerned with the Risks & Returns of both Assets!

Currency Adjusted RETURNS As investors have invested in two Assets, their Total Return will also comprise of the returns that they are able to earn on both investments: 1. Return on Foreign Asset 2. Return on Foreign Currency

Currency Adjusted RETURNS As investors have invested in two Assets, their Total Return will also comprise of the returns that they are able to earn on both investments: 1. Return on Foreign Asset 2. Return on Foreign Currency Thus, TR in Domestic terms = Return earned on Foreign Asset + Return earned on Foreign Currency Investment

Currency Adjusted RETURNS Thus, TR in Domestic terms (Approximately) = [{CF T + (P E – P B )}/P B ] Plus {Change in Foreign Currency Beginning Value of Foreign Currency}] Where, Foreign Currency is stated in DC/FC Units

Currency Adjusted RETURNS Or, Total Return in Domestic Terms (Exactly) = { RR earned on Foreign Asset Multiplied by (Ending Value of Foreign Currency/ Beginning Value of Foreign Currency)} Minus 1

Currency Adjusted RETURNS - Example An investor in Pakistan invests in Walmart at $50 when exchange rate was Rs.60/$. One year later, Walmart is $55 & there is no dividend. The Exchange rate is now Rs. 57/$. Calculate Approximate Total Return for a Pakistani investor?

Currency Adjusted RETURNS - Example An investor in Pakistan invests in Walmart at $50 when exchange rate was Rs.60/$. One year later, Walmart is $55 & there is no dividend. The Exchange rate is now Rs. 57/$. Calculate Approximate Total Return for a Pakistani investor? TR= Return on Walmart + Return on FC Return on Walmart = (55 – 50)/50 = 10% Return on FC= (57 – 60)/60 = -5% TR= 10% + (-5%) = 5%

Currency Adjusted RETURNS - Example An investor in Canada invests in Walmart (US Co.) at $35 when exchange rate was US$ 1.27/C$. One year later, Walmart is $45 & there was $5 dividend. The Exchange rate is now US$ 1.77/C$. Calculate Approximate Total Return for a Canadian investor?

Currency Adjusted RETURNS - Example An investor in Canada invests in Walmart (US Co.) at $35 when exchange rate was US$ 1.27/C$. One year later, Walmart is $45 & there was $5 dividend. The Exchange rate is now US$ 1.77/C$. Calculate Approximate Total Return for a Canadian investor? TR= Return on Walmart + Return on FC Return on Walmart = (45 – 35+5)/35 = 42.86% Return on FC= ( – )/ = % TR= 42.86% + (-28.24%) = 14.61%

Currency Adjusted RETURNS - Example An investor in Canada invests in Walmart (US Co.) at $35 when exchange rate was Pak Re 60/US$ & Pak Re 75/C$. One year later, Walmart is $45 & there was $5 dividend. The Exchange rate is now Pak Re 65/US$ & Pak Re 75/C$. Calculate Approximate Total Return for a Canadian investor?

Currency Adjusted RETURNS - Example An investor in Canada invests in Walmart (US Co.) at $35 when exchange rate was Pak Re 60/US$ & Pak Re 75/C$. One year later, Walmart is $45 & there was $5 dividend. The Exchange rate is now Pak Re 65/US$ & Pak Re 75/C$. Calculate Approximate Total Return for a Canadian investor? TR= Return on Walmart + Return on FC Return on Walmart = (45 – 35+5)/35 = 42.86% Return on FC= ( – 0.80)/0.80 = 8.34% TR= 42.86% % = 51.2%

Summary Statistics for returns Investment analysis needs statistics that are used to describe a series of returns. Two such Measures include: 1. Arithmetic Mean 2. Geometric Mean

Arithmetic Mean Arithmetic Mean = X X = Sum of all Values Number of Observations Arithmetic Mean is a better measure of performance over single periods. It is the best estimate of the expected return for next period.

Geometric Mean When percentage changes in value over time are involved, as a result of compounding, Geometric mean is needed to describe accurately the true average return over multiple periods. G = [(1+TR 1 )(1+TR 2 ) …. (1+TR N )] 1/N – 1 The Geometric Mean Returns measures the compound growth of returns over time (Multiple periods).

Arithmetic Mean Vs Geometric Mean - Example Calculate Geometric & Arithmetic Mean using following data: YearStock 1 110% 215% 3-5% 47% 510% 6-5%

Arithmetic Mean Vs Geometric Mean - Example Arithmetic Mean = ( – – 5)/6 = 5.33% Geometric Mean =[(1+0.1)(1+.15)(1+(0.05))(1+0.07)(1+.10)(1+(-0.05) ] 1/6 – 1 = 5.05%

Inflation adjusted returns Nominal Returns Real Returns

Inflation adjusted returns Nominal Returns Quoted money returns without inflation adjustments NOTE: Purchasing power is not adjusted or expressed Real Returns Inflation adjusted returns Nominal returns adjusted for inflation. Real Return = [(1+ TR)/(1+IF)] – 1 IF = inflation rate

Inflation adjusted returns - Example Suppose the nominal return on a stock is % and the inflation rate is %. What is the real return (Inflation adjusted Return)?

Inflation adjusted returns - Example Suppose the nominal return on a stock is % and the inflation rate is %. What is the real return (Inflation adjusted Return)? Real Return = (1.2857/1.0161) - 1 = – 1 = 26.53%

How do we measure Risk? The risk for one security can be calculated using the standard deviation measure. Why? Std deviation is the measure of dispersion of a data set. So, in terms of returns, std deviation actually represents RISK of that investment. The standard deviation is a reliable measure of variability The standard deviation is a measure of the total risk of an asset or portfolio.

where N is the number of returns Standard deviation of return Variance of return

Measuring Risk- Example YearStock 1 110% 215% 3-5% 47% 510% 6-5%

Measuring Risk- Example Step 1: Calculate Expected Return Exp. Return = Average of Past Returns = 32/6 = 5.33% YearStock 1 110% 215% 3-5% 47% 510% 6-5%

Measuring Risk- Example YearStock 1(X – X)(X – X) 2 110% % % % % % Sum of (X – X) 2 = Variance = /5 = Standard Deviation= (70.66) 1/2 = 8.41%

How do we use this information regarding risk? Analytical Development In Finance, decision rules are based on benchmark or alternative comparisons. Consider the statement: A: An investment (IND: X) has an ER of 35% with standard deviation of 30%

How do we use this information regarding risk? Analytical Development In Finance, decision rules are based on benchmark or alternative comparisons. Consider the statement: A: An investment (IND: X) has an ER of 35% with standard deviation of 30% B: An investment (IND: X) has an ER of 35% with standard dev of 15%

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

Risk premiums A risk premium is the additional return investors expect to receive by taking on increasing amounts of risk for example Time Premium, Default Premium, Equity Risk Premium. ERP = [(1+TR common stock) / (1+RF)] – 1

Risk premiums - Example Common stocks had a return of % over past 10 years. T-bills had a return of % over the same period. What is the historical Equity Risk Premium?

Risk premiums - Example Common stocks had a return of % over past 10 years. T-bills had a return of % over the same period. What is the historical Equity Risk Premium? ERP = ( / ) – 1 =.0578 or 5.78%

Realized Returns & Risks from Investing

Thank You for your Time & Patience Thank You for your Time & Patience

Assignment # 6 (10 Questions) Q1: Using the following data, calculate your ending wealth at the end of year 5, had you initially invested $2500: YearDividendBeginning Price Ending Price 1$ $ $ $ $4$36$30

Q2: Assuming EBIT of $2 Million, 2.5 million & 3 million under Recession, normal & Expansionary economic environment & using the following data explain how financial leverage is going to lead to more variability in ER? CurrentProposed Assets$10,000,000 Debt05,000,000 Equity10,000,0005,000,000 Debt-Equity Ratio 01 Share Price20 # of Shares500,000250,000 Interest Rate12%

Assignment # 6 (10 Questions) Q3: CWI in year 1 = , CWI in year 2 = , CWI in year 3 = , CWI in year 4 = , TR in Year 5 = 12%, CWI in year 5 = ? Q4:Suppose you invest in two Bonds when Bond A is trading at $950 with a coupon rate of 12% & Bond B is trading at 1150 with a coupon rate of 8%. After 1 year, you sell Bond A for $900 & Bond B for $1200, Calculate Relative Return for two Bonds.

Assignment # 6 (10 Questions) Q5:An investor in Canada invests in Walmart Equity at $45 when exchange rate was $60/C$. One year later, Walmart is $55 & there is a dividend of $5. The Exchange rate is now $57/C$. Calculate Exact Total Return for a Canadian investor? Q6: An investor in Japan invests in Canadian Company at C$350 when exchange rate was Euro60/C$ & Euro 35/Japanese Yen. One year later, Canadian Company is $355 & there is no dividend. The Exchange rate is now Euro57/C$ & Euro 45/Japanese yen. Calculate Approximate Total Return for a Japanese investor?

Assignment # 6 (10 Questions) Q7:In year 1, An investor in England invests in 12% Bond of Japanese Company at Japanese yen 950 when exchange rate was Euro20/UK pound & Euro 75/Japanese Yen. One year later, British Investor sold the bond at Japanese Yen 900 when The Exchange rate was Euro27/UK Pound & Euro 75/Japanese yen. At the same time, he bought a zero coupon Bond for Japanese Yen750 & a year later, sold it for Japanese Yen 800 when Exchange Rate was Euro27/UK Pound & Euro 65/Japanese yen Calculate CWI at the end of year 2 using approximate total Returns for British investor assuming initial investment was Japanese Yen 4750?

Assignment # 6 (10 Questions) Q8:In year 1, An investor in Pakistan invests in 10% Bond of Japanese Company at Japanese yen 950 when exchange rate was US$ 8.75/Pakistani Re & US$ 5.67/Japanese Yen. One year later, British Investor sold the bond at Japanese Yen 1000 when The Exchange rate was US$7.25/Pakistani Re & US$ 6.67/Japanese yen. At the same time, he bought a zero coupon Bond for Japanese Yen775 & a year later, sold it for Japanese Yen 850 when Exchange Rate was US$8.35/Pakistani Re & US$ 6.50/Japanese yen Calculate CWI at the end of year 2 using EXACT total Returns for Pakistani investor assuming initial investment was Pakistani Rs 5500?

Assignment # 6 (10 Questions) Q8:Calculate Geometric & Arithmetic Mean & Risk using following data: YearStock 1 18% 212% 3-5% 417% 512% 6-15%

Assignment # 6 (10 Questions) Q9:Common stocks had a return of % over past 10 years. T-bills had a return of % over the same period. What is the historical Equity Risk Premium? Q10: An investor in India invests in Apple’s 13% Bond at $875 when exchange rate was $60/Indian Re. One year later, Bond is trading at is $955. The Exchange rate is now $67/Indian Re. Calculate Exact Total Return for a Indian investor? Assuming that inflation Rate during the year was 12% in India & in USA it was 5%, also calculate inflation adjusted Returns for Indian investor?