Lecture 4 (Chapter 8 and 9) Flashcards
What is the difference between the Markowitz procedure and the single index model?
Markowitz Procedure is simply a framework for the estimation of risk and selection of assets in a portfolio in an efficient manner. The portfolio so selected is expected to generate highest return for a given level of risk or lowest risk for a given level of return.
Index Model, on the other hand, also establishes the relationship between risk and return. It however decomposes the influence of risk on return into systematic or market-wide risk and unsystematic or firm-specific risk.
What are the advantages of the index model compared to the Markowitz procedure for obtaining an efficiently diversified portfolio? What are its disadvantages?
Mentioned below are the advantages of Index Model in comparison to Markowitz Model:
- Less number of estimates is required for portfolio selection.
- Index Model decomposes the risk into market-wide and firm-specific components. It helps in estimation of security risk premium, thereby highlighting the power of diversification.
- It is a comparatively simple model and easy to understand.
Mentioned below is the disadvantage of Index Model in comparison to Markowitz Model:
- Index Model decomposes the risk into market-wide and firm-specific risk. However, this oversimplified classification sometimes rule out industry events that may affect many firms within an industry without affecting the economy as a whole.
For example, if two stocks in a portfolio are correlated, then index model will ignore this correlation as it considers only firm specific factors. As a result of this, portfolio variance will either be overestimated or underestimated.
What is the basic trade-off when departing from pure indexing in favor of an actively managed portfolio?
The basic trade-off when departing from pure-indexing to actively managed portfolio is the additional management fee incurred towards managing the portfolio with the possibility of superior performance of the portfolio.
Why do we call alpha a “nonmarket” return premium?
It is clear from the above mentioned equation that we call alpha a “nonmarket” return premium because it is not dependent on the market’s performance.
Why are high-alpha stocks desirable investments for active portfolio managers?
Since alpha is nonmarket return premium, high alpha stocks are desirable investments for active portfolio managers as high alpha stocks tend to rise even when the whole market falls.
With all other parameters held fixed, what would happen to a portfolio’s Sharpe ratio as the alpha of its component securities increased?
Sharpe Ratio describes that how much extra return you are getting for enduring extra volatility by holding riskier asset.
It is clear from the above equation that increases in alpha, increases the Sharpe ratio. Since portfolio alpha is the weighted average of individual securities alpha, and holding all other parameters fixed, an increase in security’s alpha results in an increase in portfolio’s Sharpe ratio.
What are the assumptions of the CAPM
- Individual behaviour
a. Investors are rational, mean-variance optimizers.
b. Their common planning horizon is a single period.
c. Investors all use identical input lists, an assumption often termed homogeneous expectations. Homogeneous expectations are consistent with the assumption that all relevant information is publicly available. - Market Structure
a. All assets are publicly held and traded on public exchanges.
c. No taxes.
d. No transaction costs.
Equilibrium of risk premium
The risk premium on the market portfolio must be just high enough to induce investors to hold the available supply of stocks. If the risk premium is too high, there will be excess demand for securities, and prices will rise; if it is too low, investors will not hold enough stock to absorb the supply, and prices will fall.
equation of market price of risk
quantifies the extra return that investors demand to bear portfolio risk.
expected return–beta relationship
the total expected rate of return is the sum of the risk-free rate (compensation for “waiting,” i.e., the time value of money) plus a risk premium (compensation for “worrying,” specifically about investment returns). Moreover, it makes a very specific prediction about the size of the risk premium: It is the product of a “benchmark risk premium” (that of the broad market portfolio) and the relative risk of the particular asset as measured by its beta (its contribution to the risk of the overall risky portfolio).
Difference between CML and SML
The CML graphs the risk premiums of efficient portfolios (i.e., portfolios composed of the market and the risk-free asset) as a function of portfolio standard deviation.
The SML, in contrast, graphs individual asset risk premiums as a function of asset risk.
More info on the SML
- The SML provides the required rate of return necessary to compensate investors for risk as well as the time value of money.
- “fairly priced” assets plot exactly on the SML; that is, their expected returns are commensurate with their risk. All securities must lie on the SML in market equilibrium.
Underpriced and overpriced securities
If a stock is perceived to be a good buy, or underpriced, it will provide an expected return in excess of the fair return stipulated by the SML. Underpriced stocks therefore plot above the SML: Given their betas, their expected returns are greater than dictated by the CAPM. Overpriced stocks plot below the SML.
Alpha of the SML
The difference between the fair and actually expected rate of return on a stock
Summary cards
-With the CAPM assumptions, all investors hold identical risky portfolios. The CAPM holds that in equilibrium the market portfolio is the unique mean-variance efficient tangency portfolio. Thus, a passive strategy is efficient.
-The CAPM market portfolio is a value-weighted portfolio. Each security is held in a proportion equal to its market value divided by the total market value of all securities.
- If the market portfolio is efficient and the average investor neither borrows nor lends, then the risk premium on the market portfolio is proportional to its variance, o^2\M, as well as the average coefficient of risk aversion across investors, A
- The CAPM implies that the risk premium on any individual asset or portfolio is the product of the risk premium on the market portfolio and the beta coefficient: E(r\i) - r\f = B\i[E(r\M) -r\f] where the beta coefficient is the covariance of the asset return with that of the market portfolio as a fraction of the variance of the return on the market portfolio
