1. 2. 3. 4. 5.

Lợi nhuận :các khái niệm cơ bản Rủi ro: các khái niệm cơ bản Rủi ro riêng lẻ Rủi ro thị trường (rủi ro danh mục) Rủi ro và lợi nhuận: CAPM/SML

1-1

Investment returns

The rate of return on an investment can be calculated as follows:

Return =

(Amount received – Amount invested) ________________________ Amount invested

For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

1-2

What is investment risk?

Two types of investment risk

Stand-alone risk Portfolio risk

Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment.

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Probability distributions

A listing of all possible outcomes, and the probability of each occurrence. Can be shown graphically.

Firm X

Firm Y -70 0 15 100

Rate of Return (%)

Expected Rate of Return

1-4

Selected Realized Returns, 1926 – 2004

Small-company stocks Large-company stocks L-T corporate bonds L-T government bonds U.S. Treasury bills Average Return 17.5% 12.4 6.2 5.8 3.8 Standard Deviation 33.1% 20.3 8.6 9.3 3.1

Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), p28.

1-5

Investment alternatives

Economy Prob. 0.1 0.2 0.4 0.2 0.1 T-Bill 5.5% 5.5% 5.5% 5.5% 5.5% HT -27.0% -7.0% 15.0% 30.0% 45.0% Coll 27.0% 13.0% 0.0% -11.0% -21.0% USR 6.0% -14.0% 3.0% 41.0% 26.0% MP -17.0% -3.0% 10.0% 25.0% 38.0%

Recession Below avg Average Above avg Boom

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Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return?

T-bills will return the promised 5.5%, regardless of the economy. No, T-bills do not provide a completely risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time. T-bills are also risky in terms of reinvestment rate risk. T-bills are risk-free in the default sense of the word.

1-7

How do the returns of HT and Coll. behave in relation to the market?

HT – Moves with the economy, and has a positive correlation. This is typical. Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual.

1-8

Calculating the expected return

^

r = expected rate of return r = ∑ ri Pi i =1 ^ N

^

r HT = (-27%) (0.1) + (-7%) (0.2) + (15%) (0.4) + (30%) (0.2) + (45%) (0.1) = 12.4%

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Summary of expected returns

HT Market USR T-bill Coll. Expected return 12.4% 10.5% 9.8% 5.5% 1.0%

HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

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Calculating standard deviation σ = Standard deviation σ = Variance = σ2 σ = (ri − ˆ)2 Pi r ∑ i =1 N

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Standard deviation for each investment σ= ∑ i =1

N

(ri − r ) 2 Pi

2 2

^

σ T − bills

(5.5 - 5.5) (0.1) + (5.5 - 5.5) (0.2) = + (5.5 - 5.5)2 (0.4) + (5.5 - 5.5)2 (0.2) + (5.5 - 5.5)2 (0.1)

1

2

σ T − bills = 0.0% σ HT = 20.0%

σ Coll = 13.2% σ USR = 18.8% σ M = 15.2%

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Comparing standard deviations

Prob. T - bill

USR HT

0

5.5 9.8

12.4

Rate of Return (%)

1-13

Comments on standard deviation as a measure of risk

Standard deviation (σi) measures total, or stand-alone, risk. The larger σi is, the lower the probability that actual returns will be closer to expected returns. Larger σi is associated with a wider probability distribution of returns.

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Comparing risk and return

Security T-bills HT Coll* USR* Market

* Seem out of place.

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Expected return, ^ r 5.5% 12.4% 1.0% 9.8% 10.5%

Risk, σ 0.0% 20.0% 13.2% 18.8% 15.2%

Coefficient of Variation (CV)

A standardized measure of dispersion