investments- risk & return

BSC/BBA IIIBSC/BBA IIISummer Semester 2010Summer Semester 2010

Lahore School of Lahore School of EconomicsEconomics

Chap 06Risks & 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

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?

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

DecisionExpected Outcome 1,2…n (return)

RISK of deviationUNCERTAINTY

Risk Calculation is based on Historical Data

T=0T=-n

What are the Sources of Risk?

An Overview

Price risk

Interest Rate risk

Market risk

Inflation risk

Business 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


An Overview Liquidity risk

Variability in ER due to inability to trade in secondary markets. 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.

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


Current Proposed

Assets $8,000,000 $8,000,000

Debt 0 4,000,000

Equity 8,000,000 4,000,000

Debt-Equity Ratio

0 1

Share Price 20 20

# of Shares 400,000 200,000

Interest Rate 10% 10%


Current Capital Structure: No DebtRecession Normal Expansion

EBIT $500,000 $1,000,000

$1,500,000

Interest ? ? ?

Net Income

? ? ?

ROE ? ? ?

EPS ? ? ?


Current Capital Structure: No DebtRecession Normal Expansion

EBIT $500,000 $1,000,000

$1,500,000

Interest 0 0 0

Net Income

500,000 1,000,000 1,500,000

ROE 6.25% 12.5% 18.75%

EPS 1.25 2.50 3.75


Proposed Capital Structure: Debt - $4 Million

Recession Normal Expansion

EBIT $500,000 $1,000,000

$1,500,000

Interest ? ? ?

Net Income

? ? ?

ROE ? ? ?

EPS ? ? ?


Proposed Capital Structure: Debt - $4 Million

Recession Normal Expansion

EBIT $500,000 $1,000,000

$1,500,000

Interest 400,000 400,000 400,000

Net Income

100,000 600,000 1,100,000

ROE 2.50% 15.50% 27.50%

EPS 0.50 3.00 5.50

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

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 + (1020-960)} / 960 = {100 + 60 }/ 960 = 0.1667 or 16.67%



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?


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?


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


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


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 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 = WI0(1+TR1)(1+TR2) … (1 + TRN)

where,

CWI = end of period wealthWI0 = 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 Return1990: 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 Return1990: 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:

1. Financial security in Foreign Country2. Foreign CurrencyThus,

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 Asset2. Return on Foreign Currency


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 Asset2. Return on Foreign Currency

Thus,

TR in Domestic terms = Return earned on Foreign Asset +

Return earned on Foreign Currency

Investment


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


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?


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 FCReturn on Walmart = (55 – 50)/50

= 10%Return on FC = (57 – 60)/60

= -5%TR = 10% + (-5%)

= 5%


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?


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 FCReturn on Walmart = (45 – 35+5)/35

= 42.86%Return on FC = (0.5650 – 0.7874)/0.7874

= -28.24%TR = 42.86% + (-28.24%)

= 14.61%


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?


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 FCReturn on Walmart = (45 – 35+5)/35

= 42.86%Return on FC = (0.8667 – 0.80)/0.80

= 8.34%TR = 42.86% + 8.34%

= 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 Mean2. Geometric Mean

Arithmetic Mean

Arithmetic Mean = X

X = Sum of all ValuesNumber 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+TR1)(1+TR2) …. (1+TRN)]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:

Year Stock 1

1 10%

2 15%

3 -5%

4 7%

5 10%

6 -5%

Arithmetic Mean Vs Geometric Mean - Example

Arithmetic Mean = (10 + 15 – 5 +7 + 10 – 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%


Nominal Returns

Real Returns


Nominal ReturnsQuoted money returns without inflation adjustments NOTE: Purchasing power is not adjusted or expressed

Real ReturnsInflation adjusted returnsNominal 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 28.5731% and the inflation rate is 1.6119%. What is the real return (Inflation adjusted Return)?

Inflation adjusted returns - Example

Suppose the nominal return on a stock is 28.5731% and the inflation rate is 1.6119%. What is the real return (Inflation adjusted Return)?

Real Return = (1.2857/1.0161) - 1= 1.2653 – 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.

1σ 1

2

2

N

RRRVar

N

ii

where N is the number of returnsStandard deviation of return

RVarRSD σ

Variance of return

Measuring Risk- Example

Year Stock 1

1 10%

2 15%

3 -5%

4 7%

5 10%

6 -5%


Step 1:Calculate Expected

ReturnExp. Return = Average

of Past Returns

= 32/6 = 5.33%

Year Stock 1

1 10%

2 15%

3 -5%

4 7%

5 10%

6 -5%


Year Stock 1 (X – X) (X – X)2

1 10% 4.67 21.81

2 15% 9.67 93.51

3 -5% -10.33 106.71

4 7% 1.67 2.79

5 10% 4.67 21.81

6 -5% -10.33 106.71

Sum of (X – X)2= 353.34

Variance = 353.34/5 = 70.66

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%




with standard deviation of 30% B: An investment (IND: X) has an ER of 35%

with standard dev of 15%




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 10.0466% over past 10 years. T-bills had a return of 4.0358% over the same period. What is the historical Equity Risk Premium?

Risk premiums - Example

Common stocks had a return of 10.0466% over past 10 years. T-bills had a return of 4.0358% over the same period. What is the historical Equity Risk Premium?

ERP = (1.100466/1.040358) – 1

= .0578 or 5.78%

Realized Returns & Risks from Investing

ThankThank YouYou for for youryour Time Time & & PatiencePatience

Assignment # 6 (10 Questions)

Q1: Using the following data, calculate your ending wealth at the end of year 5, had you initially invested $2500:Year Dividend Beginning

PriceEnding Price

1 $3 25 45

2 $5 35 40

3 $0 40 45

4 $2 45 36

5 $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?

Current Proposed

Assets $10,000,000 $10,000,000

Debt 0 5,000,000

Equity 10,000,000 5,000,000

Debt-Equity Ratio

0 1

Share Price 20 20

# of Shares 500,000 250,000

Interest Rate 12% 12%


Q3: CWI in year 1 = 1.05643, CWI in year 2 = 1.2568, CWI in year 3 = 1.5878, CWI in

year 4 = 2.3580, 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.


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?


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?


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?


Q8: Calculate Geometric & Arithmetic Mean & Risk using following data:

Year Stock 1

1 8%

2 12%

3 -5%

4 17%

5 12%

6 -15%


Q9: Common stocks had a return of 12.0866% over past 10 years. T-bills had a return of 7.0958%

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?

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