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This chapter provides an overview of the concepts of risk and return in investing. It explores the components of investment returns, including yield and capital gain, and discusses the sources of risk, such as price risk, interest rate risk, market risk, inflation risk, and business risk. Furthermore, it examines the effects of financial leverage and provides examples to illustrate the measurement of returns. Overall, this chapter aims to help investors maximize expected returns while effectively managing uncertainty.

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## Risk and Return in Investments: Maximizing Expected Returns and Managing Uncertainty

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**BSC/BBA III**Summer Semester 2010 Lahore School of Economics**Chap 06**Risks & Returns from Investing**Risk and ReturnOverview & 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**Examplesof 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**Examplesof 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) theACTUAL OUTCOMEwill be different from theEXPECTED 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**RISK of deviation UNCERTAINTY Expected Outcome 1,2…n (return) Decision T= Future T=0 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**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=CFt + (P.e – P.b) = CFT+PC PB PB**Total Return - Advantages**It is all inclusive Allows comparison b/w different assets Includes realized & unrealized gains**Total Return - Example**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 +(1020-960)}/960 ={100 + 60}/960 =0.1667or16.67%**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 = -0.0667 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+1.0 = {C + PE}/PB 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 =0.1+1 =1.1 Case 2:TR= -9.07% RR = TR +1 =-.0907+1 =0.9093**RETURN RELATIVE - Example**If Dividend paid is 13.79 & the security price is 615.93. One year earlier it was 459.27, What is the RR?**RETURN RELATIVE - Example**If Dividend paid is 13.79 & the security price is 615.93. One year earlier it was 459.27, What is the RR? RR=(615.93+13.79)/459.27 =1.3711**Cumulative Wealth Index**Cumulative wealth indexmeasures 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=WI0(1+TR1)(1+TR2)…(1 + TRN) where, CWI =end of period wealth WI0=beginning index value usually $1 TRN= Periodic TR’s in decimal form**Cumulative Wealth Index - Example**Values & Total Returns for S&P500 for past few years were as follows: Values Total Return 1990: 330.22 -3.14% 1991: 417.09 30% 1992: 435.71 7.43% 1993: 466.45 9.94% What is the CWI?**Cumulative Wealth Index - Example**Values & Total Returns for S&P500 for past few years were as follows: Values Total Return 1990: 330.22 -3.14% 1991: 417.09 30% 1992: 435.71 7.43% 1993: 466.45 9.94% What is the CWI? CWI = 1(.969)(1.3)(1.0743)(1.0994) =1.4878**Cumulative Wealth & Total return**TRN= (CWIN / CWI N-1)– 1 Where, TRN= Total Return for period N CWIN-1= Cumulative Wealth Index at period N - 1 CWIN = Cumulative Wealth Index at period N**Cumulative Wealth & Total return - Example**Suppose CWI in 2005 = 1.4878 & CWI in 2006 = 2.5787, what’s the TR in year 2006?**Cumulative Wealth & Total return - Example**Suppose CWI in 2005 = 1.4878 & CWI in 2006 = 2.5787, what’s the TR in year 2006? TR2006=(2.5787/1.4878)– 1 = 1.7332 – 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: • Financial security in Foreign Country • 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: • Return on Foreign Asset • 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: • Return on Foreign Asset • 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) = [{CFT+(PE–PB)}/PB] 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%

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