What are investment returns?

Investment returns measure the financial results of an investment.

Returns may be historical or prospective (anticipated).

Returns can be expressed in:

Dollar terms.

Percentage terms.

What is the return on an investment that costs $1,000 and is sold

after 1 year for $1,100?

Dollar return:

Percentage return:

$ Received - $ Invested $1,100 - $1,000 = $100.

$ Return/$ Invested $100/$1,000 = 0.10 = 10%.

What is investment risk?

Typically, investment returns are not known with certainty.

Investment risk pertains to the probability of earning a return less than that expected.

The greater the chance of a return far below the expected return, the greater the risk.

Assume the FollowingInvestment Alternatives

Economy Prob. T-Bill HT Coll USR MP

Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0%

Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0

Average 0.40 8.0 20.0 0.0 7.0 15.0

Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0

Boom 0.10 8.0 50.0 -20.0 30.0 43.0

1.00

What is unique about the T-bill return?

The T-bill will return 8% regardless of the state of the economy.

Is the T-bill riskless? Explain.

Calculate the expected rate of return on each alternative.

.k = k Pi i

i=1

n

k = expected rate of return.

kHT = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4%.

^

^

HT has the highest rate of return. Does that make it best?

k

HT 17.4%

Market 15.0

USR 13.8

T-bill 8.0

Collections 1.7

^

What is the standard deviationof returns for each alternative?

.Pk̂k

Variance

deviation Standard

n

1ii

2

i

2

T-bills = 0.0%.HT = 20.0%.

Coll = 13.4%.USR = 18.8%. M = 15.3%.

.Pk̂kn

1ii

2

i

HT:

= ((-22 - 17.4)20.10 + (-2 - 17.4)20.20 + (20 - 17.4)20.40 + (35 - 17.4)20.20 + (50 - 17.4)20.10)1/2 = 20.0%.

Expected Return versus Risk

Which alternative is best?

Expected

Security return Risk, HT 17.4% 20.0%

Market 15.0 15.3

USR 13.8 18.8

T-bills 8.0 0.0

Collections

1.7 13.4

Portfolio Risk and Return

Assume a two-stock portfolio with $50,000 in HT and $50,000 in Collections.

Calculate kp and p.^

Portfolio Return, kp

kp is a weighted average:

kp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.

kp is between kHT and kColl.

^

^

^

^

^ ^

^ ^

kp = wikin

i = 1

Alternative Method

kp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6%.

^

Estimated Return

(More...)

Economy Prob. HT Coll. Port.

Recession 0.10 -22.0% 28.0% 3.0%

Below avg. 0.20 -2.0 14.7 6.4

Average 0.40 20.0 0.0 10.0

Above avg. 0.20 35.0 -10.0 12.5

Boom 0.10 50.0 -20.0 15.0

p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 + (10.0 - 9.6)20.40 + (12.5 - 9.6)20.20 + (15.0 - 9.6)20.10)1/2 = 3.3%.

p is much lower than: either stock (20% and 13.4%). average of HT and Coll (16.7%).

The portfolio provides average return but much lower risk. The key here is negative correlation.

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How are betas calculated?

Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.

The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.

If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5 to

1.5. Can a stock have a negative beta?

How is beta interpreted?

Expected Return versus Market Risk

Which of the alternatives is best?

Expected

Security return Risk, b

HT 17.4% 1.29

Market 15.0 1.00

USR 13.8 0.68

T-bills 8.0 0.00

Collections

1.7 -0.86

Use the SML to calculate eachalternative’s required return.

The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM).

SML: ki = kRF + (RPM)bi . Assume kRF = 8%; kM = kM = 15%. RPM = (kM - kRF) = 15% - 8% = 7%.

^

Required Rates of Return

kHT = 8.0% + (7%)(1.29)= 8.0% + 9.0% = 17.0%.

kM = 8.0% + (7%)(1.00) = 15.0%.

kUSR = 8.0% + (7%)(0.68) = 12.8%.

kT-bill = 8.0% + (7%)(0.00) = 8.0%.

kColl = 8.0% + (7%)(-0.86) = 2.0%.

Calculate beta for a portfolio with 50% HT and 50% Collections

bp = Weighted average= 0.5(bHT) + 0.5(bColl)= 0.5(1.29) + 0.5(-0.86)= 0.22.

What is the required rate of returnon the HT/Collections portfolio?

kp = Weighted average k = 0.5(17%) + 0.5(2%) = 9.5%.

Or use SML:

kp = kRF + (RPM) bp

= 8.0% + 7%(0.22) = 9.5%.