YT: Prepnuggets, LCD comps
Introduction module
Lecture 1
Long term capital management, John Meriwether and some others
established this. Very elite group. Because of new look and scattering
nickles everybody else passed on, return was close to 40%. (1994) LTCM
drastically underestimated the risk of a profound economic crisis. LTCM
focused only on buying bonds, LTCM’s strategy was highly leveraged
and relied on historical relationships between assets, which fell apart
during the crisis. This was during the default of Russian bonds.
Portfolio return and portfolio risks
Portfolio is a colletion of assets.
Ideal: pick assets with highest expected returns.
Reality: not knowing which assets have the
highest returns.
Problem: return vs risk. You cannot have
your cake and eat it!
Pre-requisite knowledge: risk, return, risk
premium
Goal: maximize expected return and
minimize risk.
Solution: In 1952, Nobel laureate Harry Markowitz showed this is (to some
extent) possible. Modern Portfolio Theory was born!
The formula shows that when two assets have a correlation less than 1,
combining them in a portfolio reduces the portfolio’s overall risk. This is a
key
benefit of diversification—spreading investments across assets that don’t
,move exactly together lowers the portfolio’s risk compared to the simple
sum of the risks of each individual asset.
Looking at the model, we should be able
to understand that making a portfolio with
different assets moving in different
directions, combining them will have a
positive effect on the risk while
maintaining the same return.
The CAL line demonstrates the risk-return tradeoff when combining a
risk-free asset and a risky portfolio. The higher the Sharpe Ratio (the slope
of the CAL), the better the risk-adjusted return. Investors can choose
where on the CAL to invest, depending on their risk preferences. The CAL
is usually drawn as a straight line that tangentially touches the
efficient frontier of risky portfolios. The point where the CAL touches the
efficient frontier represents the optimal risky portfolio, which has the
highest Sharpe Ratio.
This means Risk premium/volatility.
Diversifiable and non-diversifiable risks
Unique risk is firm specific risk, which is diversifiable. Market risk or
systematic risk is non-diversifiable. This section comes down to placing
your money in different sectors and not putting it in one investments,
because there are fluctuations.
Optimal portfolio choises
3 steps:
- Identify risk-return combinations available from the set of risky
assets.
- Identify optimal portfolio of risky assets
- Identify a mix of risky assets and risk-free asset
Minimum variance portfolio, below the MVP has more risk lower expected
returns thus not desirable, above the MVP has more risk and higher
expected returns thus optimal portfolio candidates.
,We should combine the risky asset with the
riskfree asset.
Assumptions of CAPM: 1. Atomistic Agents, 2. homogeneous expectations,
3. publicly traded assets, 4. no transaction costs or taxes, 5.mean-variance
optimizer, 6. Risk free borrowing and lending
The Capital Asset Pricing Model (CAPM) is a framework used to
understand how the prices of financial assets are determined in
equilibrium. At its core, the CAPM explains the relationship between an
asset’s risk and its expected return, with the key assumption that
investors seek to maximize their utility by balancing risk and return.
The Starting Point: Risk and Return Tradeoff
Investors want to be compensated for the risks they take when investing
in assets. The expected return of an asset should reflect both the time
value of money and the riskiness of the cash flows. CAPM focuses on the
tradeoff between risk and return, emphasizing that the expected return on
any risky asset depends on how much market risk (also called systematic
risk) it carries.
How CAPM Works: The Market in Equilibrium
In CAPM, all investors hold the market portfolio in equilibrium, which is a
value-weighted portfolio of all available assets in the economy. The model
assumes that investors are rational, mean-variance optimizers, and they
all have the same expectations of risk and return. In equilibrium, the
market portfolio is the tangency point on the Capital Market Line (CML),
which represents the optimal combination of risk-free assets and risky
assets. The CML shows the best possible tradeoff between risk and return
, for portfolios, where the slope of the CML is the Sharpe Ratio,
representing the excess return per unit of risk.
Risk in CAPM: Systematic vs. Idiosyncratic Risk
CAPM makes a crucial distinction between systematic risk (also known
as market risk) and idiosyncratic risk (specific to an individual asset).
Systematic risk is the only type of risk that is rewarded with a risk
premium in the market because it cannot be diversified away. On the other
hand, idiosyncratic risk can be eliminated by holding a diversified portfolio,
so investors do not expect extra compensation for bearing this type of risk.
The Key Formula: CAPM Equation
The CAPM equation calculates the expected return of an asset based on its
exposure to systematic risk:
E(R_i) = R_f + beta_i (E(R_m) - R_f)
Where:
• E(R_i) is the expected return on asset i,
• r_f is the risk-free rate,
• beta_i is the asset’s beta, which measures how much the
asset moves with the overall market,
• E(R_M) is the expected return of the market portfolio,
• E(R_M) - r_f is the market risk premium.
An asset’s beta is a crucial concept in CAPM because it quantifies the
asset’s sensitivity to market movements. A beta greater than 1 means the
asset is more volatile than the market, while a beta less than 1 indicates
that the asset is less volatile.
CML vs. SML: Total Risk vs. Systematic Risk
CAPM introduces two important lines:
1. The Capital Market Line (CML), which represents the risk-
return relationship for efficient portfolios that combine a risk-free asset
and the market portfolio. The risk measure here is total risk, or standard
deviation.
2. The Security Market Line (SML), which shows the expected
return of individual assets based on their systematic risk (beta). The risk
measure on the SML is beta, as CAPM states that only systematic risk is
priced in the market.
Application and Performance Evaluation
Introduction module
Lecture 1
Long term capital management, John Meriwether and some others
established this. Very elite group. Because of new look and scattering
nickles everybody else passed on, return was close to 40%. (1994) LTCM
drastically underestimated the risk of a profound economic crisis. LTCM
focused only on buying bonds, LTCM’s strategy was highly leveraged
and relied on historical relationships between assets, which fell apart
during the crisis. This was during the default of Russian bonds.
Portfolio return and portfolio risks
Portfolio is a colletion of assets.
Ideal: pick assets with highest expected returns.
Reality: not knowing which assets have the
highest returns.
Problem: return vs risk. You cannot have
your cake and eat it!
Pre-requisite knowledge: risk, return, risk
premium
Goal: maximize expected return and
minimize risk.
Solution: In 1952, Nobel laureate Harry Markowitz showed this is (to some
extent) possible. Modern Portfolio Theory was born!
The formula shows that when two assets have a correlation less than 1,
combining them in a portfolio reduces the portfolio’s overall risk. This is a
key
benefit of diversification—spreading investments across assets that don’t
,move exactly together lowers the portfolio’s risk compared to the simple
sum of the risks of each individual asset.
Looking at the model, we should be able
to understand that making a portfolio with
different assets moving in different
directions, combining them will have a
positive effect on the risk while
maintaining the same return.
The CAL line demonstrates the risk-return tradeoff when combining a
risk-free asset and a risky portfolio. The higher the Sharpe Ratio (the slope
of the CAL), the better the risk-adjusted return. Investors can choose
where on the CAL to invest, depending on their risk preferences. The CAL
is usually drawn as a straight line that tangentially touches the
efficient frontier of risky portfolios. The point where the CAL touches the
efficient frontier represents the optimal risky portfolio, which has the
highest Sharpe Ratio.
This means Risk premium/volatility.
Diversifiable and non-diversifiable risks
Unique risk is firm specific risk, which is diversifiable. Market risk or
systematic risk is non-diversifiable. This section comes down to placing
your money in different sectors and not putting it in one investments,
because there are fluctuations.
Optimal portfolio choises
3 steps:
- Identify risk-return combinations available from the set of risky
assets.
- Identify optimal portfolio of risky assets
- Identify a mix of risky assets and risk-free asset
Minimum variance portfolio, below the MVP has more risk lower expected
returns thus not desirable, above the MVP has more risk and higher
expected returns thus optimal portfolio candidates.
,We should combine the risky asset with the
riskfree asset.
Assumptions of CAPM: 1. Atomistic Agents, 2. homogeneous expectations,
3. publicly traded assets, 4. no transaction costs or taxes, 5.mean-variance
optimizer, 6. Risk free borrowing and lending
The Capital Asset Pricing Model (CAPM) is a framework used to
understand how the prices of financial assets are determined in
equilibrium. At its core, the CAPM explains the relationship between an
asset’s risk and its expected return, with the key assumption that
investors seek to maximize their utility by balancing risk and return.
The Starting Point: Risk and Return Tradeoff
Investors want to be compensated for the risks they take when investing
in assets. The expected return of an asset should reflect both the time
value of money and the riskiness of the cash flows. CAPM focuses on the
tradeoff between risk and return, emphasizing that the expected return on
any risky asset depends on how much market risk (also called systematic
risk) it carries.
How CAPM Works: The Market in Equilibrium
In CAPM, all investors hold the market portfolio in equilibrium, which is a
value-weighted portfolio of all available assets in the economy. The model
assumes that investors are rational, mean-variance optimizers, and they
all have the same expectations of risk and return. In equilibrium, the
market portfolio is the tangency point on the Capital Market Line (CML),
which represents the optimal combination of risk-free assets and risky
assets. The CML shows the best possible tradeoff between risk and return
, for portfolios, where the slope of the CML is the Sharpe Ratio,
representing the excess return per unit of risk.
Risk in CAPM: Systematic vs. Idiosyncratic Risk
CAPM makes a crucial distinction between systematic risk (also known
as market risk) and idiosyncratic risk (specific to an individual asset).
Systematic risk is the only type of risk that is rewarded with a risk
premium in the market because it cannot be diversified away. On the other
hand, idiosyncratic risk can be eliminated by holding a diversified portfolio,
so investors do not expect extra compensation for bearing this type of risk.
The Key Formula: CAPM Equation
The CAPM equation calculates the expected return of an asset based on its
exposure to systematic risk:
E(R_i) = R_f + beta_i (E(R_m) - R_f)
Where:
• E(R_i) is the expected return on asset i,
• r_f is the risk-free rate,
• beta_i is the asset’s beta, which measures how much the
asset moves with the overall market,
• E(R_M) is the expected return of the market portfolio,
• E(R_M) - r_f is the market risk premium.
An asset’s beta is a crucial concept in CAPM because it quantifies the
asset’s sensitivity to market movements. A beta greater than 1 means the
asset is more volatile than the market, while a beta less than 1 indicates
that the asset is less volatile.
CML vs. SML: Total Risk vs. Systematic Risk
CAPM introduces two important lines:
1. The Capital Market Line (CML), which represents the risk-
return relationship for efficient portfolios that combine a risk-free asset
and the market portfolio. The risk measure here is total risk, or standard
deviation.
2. The Security Market Line (SML), which shows the expected
return of individual assets based on their systematic risk (beta). The risk
measure on the SML is beta, as CAPM states that only systematic risk is
priced in the market.
Application and Performance Evaluation
