Week 19 - Risk and Return Pt2 Flashcards
What is portfolio diversification?
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).
Why is holding 40 shares in different internet companies not true diversification?
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).
How does diversification reduce risk?
Diversification substantially reduces risk without reducing expected returns proportionally.
It minimizes unsystematic risk, which is the risk specific to individual assets or industries.
Why does diversification reduce the variability of returns?
When one asset performs worse than expected, another may perform better than expected, offsetting the impact.
This leads to more stable overall portfolio returns.
What is the minimum level of risk that cannot be diversified away?
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.
How does adding more stocks to a portfolio affect risk reduction?
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.
What happens to portfolio risk (𝜎𝑝) after adding about 40 stocks?
Portfolio standard deviation (𝜎𝑝) continues to decrease, but very slowly after about 40 stocks are included.
Further diversification has limited impact on risk reduction.
What is the minimum level of risk that diversification can achieve?
The lower limit for portfolio risk (𝜎𝑝) ≈ 20%, which equals market risk (𝜎𝑀).
This is because systematic risk cannot be eliminated through diversification.
How much risk can be eliminated by forming a well-diversified portfolio?
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.
What is the formula for total risk?
Total Risk = Systematic Risk + Unsystematic Risk
Total risk consists of both market-wide factors (systematic) and firm-specific factors (unsystematic).
What is a common measure of total risk?
Standard deviation of returns (𝜎) is used to measure total risk.
A higher standard deviation indicates greater variability in returns and higher risk.
What happens to unsystematic risk in a well-diversified portfolio?
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.
For a well-diversified portfolio, what is total risk approximately equal to?
Total risk ≈ Systematic risk because unsystematic risk is mostly eliminated.
Since systematic risk affects all assets, diversification cannot remove it.
Is there a reward for bearing risk?
Yes, there is a reward for bearing risk.
However, investors are only rewarded for systematic risk, not for avoidable risks.
What is unnecessary risk, and why is there no reward for bearing it?
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.
What determines the expected return on an asset?
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.
What is the formula for expected return based on systematic risk?
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).
What metric is used to measure systematic risk?
Systematic risk is measured by a stock’s beta coefficient (β).
Beta quantifies how much a stock moves relative to the overall market.
What does a stock’s beta represent?
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.
Is beta important for all stocks or only diversified portfolios?
Beta is relevant for stocks held in well-diversified portfolios.
Since diversification eliminates unsystematic risk, only systematic risk (measured by beta) matters.
How is beta (β) calculated?
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
What does a stock’s beta (β) indicate?
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.
What does it mean if a stock has β = 1.0?
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.
What does it mean if a stock has β > 1.0?
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).
What does it mean if a stock has β < 1.0?
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).
What is the usual range of beta values for most stocks?
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.
What is the beta of the overall market?
The market beta is always β = 1.0.
Formula:
β_M = σ_M,M / σˆ2_M = p_M,M σ_M / σ_M = 1
What is the beta of a risk-free asset like a T-Bill?
T-Bills have β = 0 because they have no market risk.
Their return is fixed, so they do not react to market fluctuations.
- Which security has more total risk?
- Which security has more systematic risk?
- Which security should have higher expected return?
Security A: Std = 20%, Beta = 1.25
Security B: Std = 30%, Beta = 0.95
- 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. - 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. - 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
How is the risk premium calculated?
Risk premium = Expected return – Risk-free rate
Rist premium = E(R) - r_f
It represents the extra return investors demand for taking on risk.
How does beta (β) affect the risk premium?
The higher the beta, the greater the risk premium should be.
Since beta measures systematic risk, investors require higher returns for riskier assets.
Can we define a mathematical relationship between risk premium and beta?
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
What does CAPM imply about expected returns?
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.
How is the reward-to-risk ratio calculated?
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.
What should happen to the reward-to-risk ratio in equilibrium?
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.
What happens when expected return (E(R)) is plotted against beta (β)?
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
What does the Security Market Line (SML) represent?
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).
What is the condition for market equilibrium regarding the reward-to-risk ratio?
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.
What is the beta of the market?
The beta of the market (β_M) is always 1.
This is because the market’s systematic risk is considered the benchmark (market risk).
How can we solve for E(R_A) (the expected return of asset A) using market equilibrium?
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.
What does the equation E(R_A) = R_f + β_A x (E(R_M) - R_f) mean?
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.
What does the Capital Asset Pricing Model (CAPM) define?
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.
What is the formula for the expected return (E(R_i)) of an asset according to CAPM?
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).
What is the market risk premium in the CAPM formula?
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.
How can CAPM and the SML be used to determine an asset’s expected return?
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.
What does the formula E(R_i) = r_f + β_i x (E(R_M) - r_f) represent?
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
What does the risk-free rate (r_f) measure?
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.
What does the market risk premium R_PM represent?
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.
What does β_i measure in the CAPM formula?
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.
