Salaar - Finance

INVESTMENTSINVESTMENTS

BBASUMMER 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=0T=-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 riskVariability 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 RiskAverage annualstandard deviation (%)

Number of stocksin portfolio

Diversifiable risk (unique risk)

Non-diversifiablerisk (market risk)

49.2

23.9

19.2

1 10 20 30 40 1000

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

1σ 1

2

2

N

RRRVar

N

ii

where N is the number of returns

Standard deviation of return

RVarRSD σ

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 PremiumAdditional Compensation for assuming risk

Equity Risk PremiumDifference 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 # 9 Calculating ERP

Common stocks had a return of 10.0466% over 80yrs. T-bills had a return of 4.0358% over the same period.

a) What is the historical Equity Risk Premium?

Salaar - Finance

PROBLEM # 9 Calculating ERPCommon stocks had a return of 10.0466% over 80yrs. T-bills had a return of 4.0358% over the same period.

a) What is the historical Equity Risk Premium?

ERP = 1.100466/1.040358 – 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 RETURNSTR

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 RETURNSAdvantages of TR

Gives a measure of return in %

Allows comparison b/w different assets

Includes realized & unrealized gains

Salaar - Finance

PROBLEM # 1 Example 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 # 1 Example 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+(1020-960) / 960 = 100+60 / 960 = 0.1667 or 16.67%

Salaar - Finance

PROBLEM # 2 Example 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 # 2 Example 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 = -0.0667 = (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 + 1.0

Therefore,

TR in decimal = RR – 1.0

Since its expressed as 1 base, modified TR

RR = (C+ Pe) / Pb

Salaar - Finance

PROBLEM # 3 Example RR

If the TR is 10%, & -9.07% then,

a) What is the RR?

Salaar - Finance

PROBLEM # 3 Example RR

If the TR is 10%, & -9.07% then,

a) What is the RR?

10% TR, RR = TR + 1 = 0.1 + 1 = 1.1-9.07% TR, RR = TR + 1 = -.0907 + 1 = 0.9093

Salaar - Finance

PROBLEM # 4 Example RR

If the Dividend is 13.79 & the security price is 615.93. One year earlier it was 459.27,

a) What is the RR?

Salaar - Finance

PROBLEM # 4 Example RR

If the Dividend is 13.79 & the security price is 615.93. One year earlier it was 459.27,

a) What is the RR?

RR = (615.93 – 459.27 + 13.79) / 459.27 = 1.3711

Salaar - Finance

MEASURING RETURNS

Cumulative Wealth Index

CWICumulative 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 # 5 Example of CWI

The values of the S&P were as follows:1990 = 330.22 & TR= -3.14%1991 = 417.09 = 30%1992 = 435.71 = 7.43%1993 = 466.45 = 9.94%

a) What are the Return Relatives?

b) What is the CWI?

Salaar - Finance

PROBLEM # 5 Example of CWI

The values of the S&P were as follows:1990 = 330.22 & TR = -3.14%1991 = 417.09 = 30%1992 = 435.71 = 7.43%1993 = 466.45 = 9.94%

a)What are the Return Relatives? RR’s = -.0314+1=0.969, 0.3+1=1.3, 0.0743+1=1.0743, 0.0994+1=1.0994

b) What is the CWI? 1(.969)(1.3)(1.0743)(1.0994) = 1.4878

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 # 6 Getting TR from CWI

Suppose CWI,2005 = 1.4878 & CWI,2006 = 2.5787,

a) what’s the TR?

Salaar - Finance

PROBLEM # 6 Getting TR from CWI

Suppose CWI,2005 = 1.4878 & CWI,2006 = 2.5787,

a) what’s the TR?

2.5787/1.4878 – 1 = 1.7332 – 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 # 8 FX returnsSuppose 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 # 8 FX returnsSuppose 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 – 1 = .045 = 4.5%.

Salaar - Finance

Some Realities of risk in the real world

Realized Returns Over Long Periods(1920-2002)

• 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