6 Matching Annotations
1. Oct 2020
2. en.wikipedia.org en.wikipedia.org
1. The Y-intercept of the SML is equal to the risk-free interest rate. The slope of the SML is equal to the market risk premium and reflects the risk return tradeoff at a given time: S M L : E ( R i ) = R f + β i [ E ( R M ) − R f ] {\displaystyle \mathrm {SML} :E(R_{i})=R_{f}+\beta _{i}[E(R_{M})-R_{f}]\,} where: E(Ri) is an expected return on security E(RM) is an expected return on market portfolio M β is a nondiversifiable or systematic risk RM is a market rate of return Rf is a risk-free rate

This is one statement of the key relationship.

The point is that the market will have a single tradeoff between unavoidable (nondiversifiable) risk and return.

Asset's returns must reflect this, according to the theory. Their prices will be bid up (or down), until this is the case ... the 'arbitrage' process.

Why? Because (assuming borrowing/lending at a risk free rate) *any investor can achieve a particular return for a given risk level simply by buying the 'diversified market basket' and leveraging this (for more risk) or investing the remainder in the risk free-asseet (for less risk). (And she can do no better than this.)

2. This abnormal extra return above the market's return at a given level of risk is what is called the alpha.

this is why you here the stock-touts bragging about their 'alpha'

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3. en.wikipedia.org en.wikipedia.org
1. Capital asset pricing model

please read this article

2. quantity beta (β)

You hear about this 'beta' all the time as the measure of 'the correlation of the risk of an asset with the representative market basket'...

but confusingly, $$\beta$$ is used to represent the slope of the expected return of an asset as this risk increases.

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4. en.wikipedia.org en.wikipedia.org
1. If the fraction q {\displaystyle q} of a one-unit (e.g. one-million-dollar) portfolio is placed in asset X and the fraction 1 − q {\displaystyle 1-q} is placed in Y, the stochastic portfolio return is q x + ( 1 − q ) y {\displaystyle qx+(1-q)y} . If x {\displaystyle x} and y {\displaystyle y} are uncorrelated, the variance of portfolio return is var ( q x + ( 1 − q ) y ) = q 2 σ x 2 + ( 1 − q ) 2 σ y 2 {\displaystyle {\text{var}}(qx+(1-q)y)=q^{2}\sigma _{x}^{2}+(1-q)^{2}\sigma _{y}^{2}} . The variance-minimizing value of q {\displaystyle q} is q = σ y 2 / [ σ x 2 + σ y 2 ] {\displaystyle q=\sigma _{y}^{2}/[\sigma _{x}^{2}+\sigma _{y}^{2}]} , which is strictly between 0 {\displaystyle 0} and 1 {\displaystyle 1} . Using this value of q {\displaystyle q} in the expression for the variance of portfolio return gives the latter as σ x 2 σ y 2 / [ σ x 2 + σ y 2 ] {\displaystyle \sigma _{x}^{2}\sigma _{y}^{2}/[\sigma _{x}^{2}+\sigma _{y}^{2}]} , which is less than what it would be at either of the undiversified values q = 1 {\displaystyle q=1} and q = 0 {\displaystyle q=0} (which respectively give portfolio return variance of σ x 2 {\displaystyle \sigma _{x}^{2}} and σ y 2 {\displaystyle \sigma _{y}^{2}} ). Note that the favorable effect of diversification on portfolio variance would be enhanced if x {\displaystyle x} and y {\displaystyle y} were negatively correlated but diminished (though not eliminated) if they were positively correlated.

Key building block formulae.

• Start with 'what happens to the variance when we combine two assets (uncorrelated with same expected return)'

• What are the variance minimizing shares and what is the resulting variance of the portfolio.

2. Similarly, a 1985 book reported that most value from diversification comes from the first 15 or 20 different stocks in a portfolio.

the conventional wisdom is that there are sharply diminishing returns to this diversification