W1 and recap
Diversification: the averaging out of independent risks in a large portfolio. Risk premium of
diversifiable risk is zero
The risk premium of a security is determined by its systematic risk and does not depend on
diversifiable risk
Efficient portfolio contains only systematic risk
Positive covariance: two returns tend to move together
Identifying efficient portfolio, the highest possible expected return: Sharpe Ratio
Combinations of risk free asset and this portfolio provide the best risk and return tradeoff available,
where an investor’s preference determines how much to invest in each
YTM: the interest rate that makes the present value of the bond’s payments equal to its price
Risk averse: A>0
Markowitz portfolio selection model, Mutual fund separation theorem: two independent tasks:
1. Determination of the optimal risky portfolio: purely technical
2. Determination of the complete portfolio: capital allocation between risk-free and risky
depends on personal preference
Challenges:
1. A large number of parameters
2. Danger of errors in estimating correlation coefficients and risk premia
3. Investors may define risk differently and may have richer preferences than risk
Index model helps solving those challenges: it accounts in a tractable way for sources of risk and
decomposes uncertainty into systematic and idiosyncratic risk
Article: what drives risk perception
- online experiment with financial professionals and lay people
- do not use standard deviations, but skewness of stock as measure for risk, because of a
behavioral bias: loss aversion, we fear losses, losses and gains are not experienced
symmetrically
- results suggest
o that a single higher moment cannot predict variation in risk perception
o risk perception does not differ significantly between financial professionals and
laymen and also not between countries
o one of the more complex risk measures, loss probabilities, had the highest
explanatory power: it explains more than 75% (risk perception) and even more than
95% of the variation in means
Article: why heuristics work
- 1/N heuristic: allocate resources equally to each of N alternatives
o ecologically rational if: high unpredictability, small learning sample, large N
o bold prediction: can outperform optimal asset allocation models
- How can 1/N heuristic be better than portfolio optimization
, o Portfolio optimization models often overfit, and thus perform worse at predicting the
future, whereas the 1/N heuristic does not estimate and cannot overfit
o Three relevant environmental features determine when 1/N predicts the future
better:
The predictive uncertainty of the problem. The larger the uncertainty, the
greater the advantage of 1/N
The (panel) size of the learning sample. The smaller, the greater
Number (N) of assets: the larger, the greater the advantage
- Imitate the successful heuristic: look for the most successful person and imitate this behavior
o Ecologically rational if: individual learning slow, info search costly and time
consuming
o Bold predictions: cultural evolution
Perfect negative correlation: minimum variance is zero, since correlation is -1
Week 2
A portfolio is efficient if and only if the expected return of every available security equals its required
return
Self-financing portfolio: can be obstructed by going long in some stocks and going short in other
stocks with equal MV
Selecting a portfolio:
1. SMB portfolio: long small stocks, short large stocks
2. HML portfolio: long high-BM stocks, short low-BM stocks
a. BM value greater than 70th percentile NYSE firms and finance this with BM ratio less
than 30th percentile NYSE stocks
3. Momentum portfolio: buy top 30% of stock and finance this by short selling bottom 30%
a. Holding one year
Markowitz needs many estimates
- we need 2n+(n2-n)/2 parameters:
o n estimates of expected returns
o n estimates of return standard deviations
o (n2-n)/2 estimates of correlations
- with large n:
o large estimation error
o large data requirements
parameters needed for the SIM
- we need 3n+2 parameters
CAPM:
- In eqm all investors hold the same portfolio, the market portfolio. This is the tangency
portfolio, where the capital market line is the best attainable capital allocation line.
Arbitrage Pricing Theory APT: predicts a SML linking expected returns to risk, relies on three
assumptions:
Diversification: the averaging out of independent risks in a large portfolio. Risk premium of
diversifiable risk is zero
The risk premium of a security is determined by its systematic risk and does not depend on
diversifiable risk
Efficient portfolio contains only systematic risk
Positive covariance: two returns tend to move together
Identifying efficient portfolio, the highest possible expected return: Sharpe Ratio
Combinations of risk free asset and this portfolio provide the best risk and return tradeoff available,
where an investor’s preference determines how much to invest in each
YTM: the interest rate that makes the present value of the bond’s payments equal to its price
Risk averse: A>0
Markowitz portfolio selection model, Mutual fund separation theorem: two independent tasks:
1. Determination of the optimal risky portfolio: purely technical
2. Determination of the complete portfolio: capital allocation between risk-free and risky
depends on personal preference
Challenges:
1. A large number of parameters
2. Danger of errors in estimating correlation coefficients and risk premia
3. Investors may define risk differently and may have richer preferences than risk
Index model helps solving those challenges: it accounts in a tractable way for sources of risk and
decomposes uncertainty into systematic and idiosyncratic risk
Article: what drives risk perception
- online experiment with financial professionals and lay people
- do not use standard deviations, but skewness of stock as measure for risk, because of a
behavioral bias: loss aversion, we fear losses, losses and gains are not experienced
symmetrically
- results suggest
o that a single higher moment cannot predict variation in risk perception
o risk perception does not differ significantly between financial professionals and
laymen and also not between countries
o one of the more complex risk measures, loss probabilities, had the highest
explanatory power: it explains more than 75% (risk perception) and even more than
95% of the variation in means
Article: why heuristics work
- 1/N heuristic: allocate resources equally to each of N alternatives
o ecologically rational if: high unpredictability, small learning sample, large N
o bold prediction: can outperform optimal asset allocation models
- How can 1/N heuristic be better than portfolio optimization
, o Portfolio optimization models often overfit, and thus perform worse at predicting the
future, whereas the 1/N heuristic does not estimate and cannot overfit
o Three relevant environmental features determine when 1/N predicts the future
better:
The predictive uncertainty of the problem. The larger the uncertainty, the
greater the advantage of 1/N
The (panel) size of the learning sample. The smaller, the greater
Number (N) of assets: the larger, the greater the advantage
- Imitate the successful heuristic: look for the most successful person and imitate this behavior
o Ecologically rational if: individual learning slow, info search costly and time
consuming
o Bold predictions: cultural evolution
Perfect negative correlation: minimum variance is zero, since correlation is -1
Week 2
A portfolio is efficient if and only if the expected return of every available security equals its required
return
Self-financing portfolio: can be obstructed by going long in some stocks and going short in other
stocks with equal MV
Selecting a portfolio:
1. SMB portfolio: long small stocks, short large stocks
2. HML portfolio: long high-BM stocks, short low-BM stocks
a. BM value greater than 70th percentile NYSE firms and finance this with BM ratio less
than 30th percentile NYSE stocks
3. Momentum portfolio: buy top 30% of stock and finance this by short selling bottom 30%
a. Holding one year
Markowitz needs many estimates
- we need 2n+(n2-n)/2 parameters:
o n estimates of expected returns
o n estimates of return standard deviations
o (n2-n)/2 estimates of correlations
- with large n:
o large estimation error
o large data requirements
parameters needed for the SIM
- we need 3n+2 parameters
CAPM:
- In eqm all investors hold the same portfolio, the market portfolio. This is the tangency
portfolio, where the capital market line is the best attainable capital allocation line.
Arbitrage Pricing Theory APT: predicts a SML linking expected returns to risk, relies on three
assumptions:
