Week 19 - Risk and Return Pt2

Question 1

What is portfolio diversification?

Answer 1

Portfolio diversification is the process of investing in several different assets or sectors to reduce risk.

It works best when assets have less than perfectly positive correlation (i.e., they don’t move in the same direction all the time).

Question 2

Why is holding 40 shares in different internet companies not true diversification?

Answer 2

Not truly diversified because all companies belong to the same industry and will likely move together.

True diversification is achieved by investing in 40 firms across different industries (e.g., technology, healthcare, energy, finance).

Question 3

How does diversification reduce risk?

Answer 3

Diversification substantially reduces risk without reducing expected returns proportionally.

It minimizes unsystematic risk, which is the risk specific to individual assets or industries.

Question 4

Why does diversification reduce the variability of returns?

Answer 4

When one asset performs worse than expected, another may perform better than expected, offsetting the impact.

This leads to more stable overall portfolio returns.

Question 5

What is the minimum level of risk that cannot be diversified away?

Answer 5

The minimum risk that remains after diversification is called systematic risk.

Since systematic risk affects all assets (e.g., inflation, interest rates, recessions), it cannot be eliminated through diversification.

Question 6

How does adding more stocks to a portfolio affect risk reduction?

Answer 6

As more stocks are added, each additional stock has a smaller impact on reducing total portfolio risk.

The benefits of diversification diminish after a certain point.

Question 7

What happens to portfolio risk (𝜎𝑝) after adding about 40 stocks?

Answer 7

Portfolio standard deviation (𝜎𝑝) continues to decrease, but very slowly after about 40 stocks are included.
Further diversification has limited impact on risk reduction.

Question 8

What is the minimum level of risk that diversification can achieve?

Answer 8

The lower limit for portfolio risk (𝜎𝑝) ≈ 20%, which equals market risk (𝜎𝑀).
This is because systematic risk cannot be eliminated through diversification.

Question 9

How much risk can be eliminated by forming a well-diversified portfolio?

Answer 9

A well-diversified portfolio can eliminate about half the risk of owning a single stock.

The remaining risk is systematic risk, which affects the entire market.

Question 10

What is the formula for total risk?

Answer 10

Total Risk = Systematic Risk + Unsystematic Risk
Total risk consists of both market-wide factors (systematic) and firm-specific factors (unsystematic).

Question 11

What is a common measure of total risk?

Answer 11

Standard deviation of returns (𝜎) is used to measure total risk.

A higher standard deviation indicates greater variability in returns and higher risk.

Question 12

What happens to unsystematic risk in a well-diversified portfolio?

Answer 12

Unsystematic risk becomes very small because diversification reduces firm-specific risks.

The more diversified the portfolio, the less impact unsystematic risk has on total risk.

Question 13

For a well-diversified portfolio, what is total risk approximately equal to?

Answer 13

Total risk ≈ Systematic risk because unsystematic risk is mostly eliminated.

Since systematic risk affects all assets, diversification cannot remove it.

Question 14

Is there a reward for bearing risk?

Answer 14

Yes, there is a reward for bearing risk.
However, investors are only rewarded for systematic risk, not for avoidable risks.

Question 15

What is unnecessary risk, and why is there no reward for bearing it?

Answer 15

Unnecessary risk = Unsystematic risk, which can be diversified away.

Investors do not receive extra return for taking risks that could have been eliminated through diversification.

Question 16

What determines the expected return on an asset?

Answer 16

The expected return (also called the market-required return) depends only on the asset’s systematic risk.

Since unsystematic risk can be diversified away, it does not affect expected returns.

Question 17

What is the formula for expected return based on systematic risk?

Answer 17

Expected Return = Risk-Free Rate + Risk Premium

The risk premium is based only on systematic risk, as measured by beta (β) in the Capital Asset Pricing Model (CAPM).

Question 18

What metric is used to measure systematic risk?

Answer 18

Systematic risk is measured by a stock’s beta coefficient (β).

Beta quantifies how much a stock moves relative to the overall market.

Question 19

What does a stock’s beta represent?

Answer 19

A stock’s beta (β) shows its contribution to the overall riskiness of a diversified portfolio.
Higher beta → Stock is more volatile than the market.
Lower beta → Stock is less volatile than the market.

Question 20

Is beta important for all stocks or only diversified portfolios?

Answer 20

Beta is relevant for stocks held in well-diversified portfolios.
Since diversification eliminates unsystematic risk, only systematic risk (measured by beta) matters.

Question 21

How is beta (β) calculated?

Answer 21

β_i = σ_i,M / σˆ2_M = p_i,M σ_i / σ_M

σ_i,M - Covariance between stock i and the market
σˆ2_M - Variance of the market return
p_i,M - Correlation between stock i and the market
σ_i - Standard deviation of stock i
σ_M - Standard deviation of the market

Question 22

What does a stock’s beta (β) indicate?

Answer 22

Beta (β) measures a stock’s systematic risk relative to the market.

It shows how much the stock’s return moves in response to market movements.

Question 23

What does it mean if a stock has β = 1.0?

Answer 23

The stock has average market risk.
It tends to move in line with the market.
If the market goes up 10%, the stock is expected to rise 10%, and vice versa.

Question 24

What does it mean if a stock has β > 1.0?

Answer 24

The stock is riskier than average (more volatile than the market).
It tends to amplify market movements.
Example: If β = 1.5, and the market rises 10%, the stock is expected to rise 15% (and vice versa for losses).

Question 25

What does it mean if a stock has β < 1.0?

Answer 25

The stock is less risky than average (less volatile than the market). It moves slower than the market. Example: If β = 0.5, and the market rises 10%, the stock is expected to rise 5% (and vice versa for losses).

Question 26

What is the usual range of beta values for most stocks?

Answer 26

Most stocks have betas between 0.5 and 1.5. High-growth stocks (tech firms) often have β > 1.0. Defensive stocks (utilities, consumer staples) often have β < 1.0.

Question 27

What is the beta of the overall market?

Answer 27

The market beta is always β = 1.0. Formula: β_M = σ_M,M / σˆ2_M = p_M,M σ_M / σ_M = 1

Question 28

What is the beta of a risk-free asset like a T-Bill?

Answer 28

T-Bills have β = 0 because they have no market risk. Their return is fixed, so they do not react to market fluctuations.

Question 29

1. Which security has more total risk? 2. Which security has more systematic risk? 3. Which security should have higher expected return? Security A: Std = 20%, Beta = 1.25 Security B: Std = 30%, Beta = 0.95

Answer 29

1. Total risk is measured by standard deviation (σ), which captures both systematic and unsystematic (firm-specific) risk. Since Security B has a higher standard deviation, it has more total risk. 2. Systematic risk is measured by beta (β), which indicates how much the security moves with the market. Since Security A has a higher beta, it has more systematic risk. 3. According to the CAPM formula: E(R_i) = R_f + β_i (E(R_m) - R_f) where only systematic risk (beta) affects expected return. Since Security A has a higher beta (1.25) than Security B (0.95), Security A should have the higher expected return

Question 30

How is the risk premium calculated?

Answer 30

Risk premium = Expected return – Risk-free rate Rist premium = E(R) - r_f It represents the extra return investors demand for taking on risk.

Question 31

How does beta (β) affect the risk premium?

Answer 31

The higher the beta, the greater the risk premium should be. Since beta measures systematic risk, investors require higher returns for riskier assets.

Question 32

Can we define a mathematical relationship between risk premium and beta?

Answer 32

Yes! The Capital Asset Pricing Model (CAPM) defines this relationship. Expected return is calculated as: E(R) = r_f + β (E(R_M) - r_f) r_f - risk free rate E(R_M) - expected market return β - systematic risk measure

Question 33

What does CAPM imply about expected returns?

Answer 33

The only factor affecting a stock’s expected return (above r_f) is its beta. Stocks with higher beta require higher expected returns to compensate for risk. Risk that can be diversified away (unsystematic risk) does not influence expected return.

Question 34

How is the reward-to-risk ratio calculated?

Answer 34

The reward-to-risk ratio is given by: (E(R_A) - R_f) / β_A This measures the extra return per unit of systematic risk (β). It represents the slope of the risk-return tradeoff line.

Question 35

What should happen to the reward-to-risk ratio in equilibrium?

Answer 35

In equilibrium, the reward-to-risk ratio should be the same for all assets. If one asset had a higher ratio, investors would buy it, increasing its price and lowering its expected return until equilibrium is restored.

Question 36

What happens when expected return (E(R)) is plotted against beta (β)?

Answer 36

The result should be a straight line. This is known as the Security Market Line (SML). The slope of the SML is the market risk premium: E(R_M) - R_f

Question 37

What does the Security Market Line (SML) represent?

Answer 37

The SML shows the required return for a given level of systematic risk (β). If an asset is above the SML, it is undervalued (higher return for its risk). If an asset is below the SML, it is overvalued (lower return for its risk).

Question 38

What is the condition for market equilibrium regarding the reward-to-risk ratio?

Answer 38

In equilibrium, all assets and portfolios must have the same reward-to-risk ratio. This ratio for each asset must equal the ratio for the market: (E(R_A) - R_f)/ β_A = (E(R_M) - R_f )/ β_M The ratio is the same for all assets, meaning investors receive equal compensation for taking on risk.

Question 39

What is the beta of the market?

Answer 39

The beta of the market (β_M) is always 1. This is because the market’s systematic risk is considered the benchmark (market risk).

Question 40

How can we solve for E(R_A) (the expected return of asset A) using market equilibrium?

Answer 40

From the equilibrium condition, solving for E(R_A) gives: E(R_A) - R_f = β_A x (E(R_M) - R_f) Rearranged it becomes: E(R_A) = R_f + β_A x (E(R_M) - R_f) E(R_A) is the risk-free rate plus the asset’s beta times the market risk premium.

Question 41

What does the equation E(R_A) = R_f + β_A x (E(R_M) - R_f) mean?

Answer 41

The expected return (E(R_A)) on asset A is determined by: The risk-free rate (R_f). The asset’s beta (β_A), which reflects its systematic risk. The market risk premium (difference between the market return and the risk-free rate). A higher beta means higher expected return, as the asset is riskier.

Question 42

What does the Capital Asset Pricing Model (CAPM) define?

Answer 42

CAPM defines the relationship between risk and return for any asset. It shows how an asset's expected return is related to its systematic risk (beta). It uses the Security Market Line (SML) to plot the risk-return tradeoff.

Question 43

What is the formula for the expected return (E(R_i)) of an asset according to CAPM?

Answer 43

The CAPM formula is: E(R_i) = r_f + β_i x (E(R_M) - r_f) E(R_i) - expected return of asset i r_f - risk-free rate β_i - systematic risk (beta) of asset i E(R_M) - r_f - market risk premium (the difference between the market return and the risk-free rate).

Question 44

What is the market risk premium in the CAPM formula?

Answer 44

The market risk premium is the difference between the market return E(R_M) and the risk-free rate r_f: E(R_M) - r_f It represents the extra return expected from the market for bearing systematic risk.

Question 45

How can CAPM and the SML be used to determine an asset’s expected return?

Answer 45

If an asset’s systematic risk (β_i) is known, CAPM and the SML can be used to calculate its expected return (E(R_i)). By knowing the asset’s beta, you can apply the CAPM formula to determine the return required by investors for bearing that level of risk.

Question 46

What does the formula E(R_i) = r_f + β_i x (E(R_M) - r_f) represent?

Answer 46

The formula shows how the required return for an asset E(R_i) is determined by: r_f - the risk-free rate, which measures the pure time value of money β_i - the asset's systematic risk (how it moves relative to the market E(R_M) - r_f - the market risk premium, representing the reward for bearing systematic risk

Question 47

What does the risk-free rate (r_f) measure?

Answer 47

The risk-free rate (r_f) measures the pure time value of money. It is the return on an investment with zero risk, typically represented by the return on Treasury bills or government bonds.

Question 48

What does the market risk premium R_PM represent?

Answer 48

The market risk premium R_PM = E(R_M) - r_F measures the reward for bearing systematic risk. It represents the extra return investors expect from investing in the market instead of a risk-free asset.

Question 49

What does β_i measure in the CAPM formula?

Answer 49

β_i measures the amount of systematic risk an asset has relative to the overall market. It reflects how the asset’s return moves with the market’s return. β_i = 1 - The asset moves with the market. β_i > 1 - The asset is more volatile than the market. β_i < 1 - The asset is less volatile than the market.