The Formulas - Portfolio Theory
The formulas:
CAPM: E(rx)=rf+beta[E(rm)-rf) --> E(rx)=rf+beta[MRP]
Weighted portfolio one risky asset: ERp=Wr(ERr)+(1-Wr)(ERf)
Weighted protfolio two risky assets: ERp=Wf(ERf)+(1-Wf)[(Pa)(ERa)+(Pb)(ERb)]
Correlation coefficient=Covariance/(SDa)(SDb)
Variance of portfolio: (SDa)^2(Wa)^2+(SDb)^2(Wb)+2(Wa)(SDa)(Wb)(SDb)(CorrCoeff)
Risk aversion: E(rp)-rf=.005A X Variance --> A=E(rp)-rf/.005 X Variance --> A=Risk Premium/.005 X Variance
Reward to variability ratio: Risk Premium/Standard deviation - this one should be intuiive
7:58:15 PM     comment []

My life for the past several days
HPR-Holding Period return-Rate of return over a given investment period=EP-BP/BP=Return/Investment. Arithmetic Average-The sum of returns in each period divided by the number of periods. Geometric Average-The single per-period return that gives the same cumulative performance as the sequence of actual returns=(1+a)(a+b)(?)1/n-1. Dollar-weighted average return=Internal rate of return on an investment. Scenario analysis-Process of devising a list of possible economic scenarios and specifying the likelihood of each one, as well as the HPR that will be realized in each case. Probability distribution-list of possible outcomes with associated probabilities. Expected return-the reward from an investment-.25X44%+.50X14%+.25X(-16%)=14% Variance-the expected value of the squared deviation from the mean-.24X(44-12)2+.50X(14-14)2+.25X(-16-14)2=450. Standard Deviation-the square root of the variance-sqt(450)=21.21. Risk-free rate-the rate of return that can be earned with certainty. Risk premium-an expected return in excess of that on risk-free securities. Risk aversion-reluctance to accept risk. A=rp/.005Xvar. asset allocation-portfolio choice among broad investment classes. Complete portfolio-the entire portfolio including risky and risk-free assets. Capital allocation line-plot of risk-return combinations available by varying portfolio allocation between a risk-free asset and a risky portfolio. Reward-to-variability ratio-ratio of risk premium to standard deviation=rp/sd. Capital market line-CAL using market idx. Market risk, systematic risk, nondiversifiable risk-risk factors common to the whole economy. Unique risk, firm-specific risk, nonsystematic risk, diversifiable risk-risk that can be eliminated by diversification. Investment opportunity set-set of available portfolio risk-return combinations. Optimal risky portfolio-the best combination of risky assets to be mixed with safe assets to form the complete portfolio. Efficient frontier-graph representing a set of portfolios that maximizes expected return at each level of portfolio risk. Separation property-the property that implies portfolio choice can be separated into two independent tasks: determination of the optimal risky portfolio, which is a purely technical problem, and the personal choice of the best mix of the risky portfolio and the risk-free asset. Factor model-statistical model to measure the firm-specific versus systematic risk of a stocks rate of return. Excess return-rate of return in excess of the risk-free rate. Beta-the sensitivity of a security?s returns to the systematic or market factor. Index model-a model of stock returns using a market index such as the S&P to represent common or systematic risk factors. Security characteristic line-plot of a security?s excess return as a function of the excess return of the market. Capital asset pricing model(CAPM)-William F. Sharpe-a model that relates the required rate of return for a security to its risk as measured by beta. Market portfolio-the portfolio for which each security is held in proportion to its market value. Mutual fund theorem-states that all investors desire the same portfolio of risky assets and can be satisfied by a single mutual fund comprised of that portfolio. Expected return-beta relationship-implication of the CAPM that security risk premiums will be proportional to beta. Security market line-graphical representation of the expected return-beta relationship of the CAPM. Alpha-the abnormal rate of return on a security in excess of what would be predicted by an equilibrium model such as CAPM or APT. Security characteristic line-a plot of a security?s expected excess return over the risk-free rate as a function of the excess return on the market. Arbitrage-Stephen Ross-creation of riskless profits made possible by relative mispricing among securities. Zero-investment portfolio-a portfolio of zero net value, established by buying and shorting component securities, usually in the context of an arbitrage strategy. Arbitrage pricing theory-a theory of risk-return relationships derived from no-arbitrage considerations in large capital markets. Well-diversified portfolio-a portfolio sufficiently diversified that nonsystematic risk is negligible. Factor portfolio-a well-diversified portfolio constructed to have a beta of 1.0 on one factor and a beta of zero any other factor. Random walk-the notion that stock price changes are random and unpredictable. Efficient market hypothesis-the hypothesis that prices of securities fully reflect available information about securities. Weak-form EMH-The assertion that stock prices already reflect all information contained in the history of past trading. Semistrong-form EMH-The assertion that stock prices already reflect all publicly available information. Strong-form EMH-the assertion that stock prices reflect all relevant information, including insider trading. Technical analysis-research on recurrent and predictable stock price patterns and on proxies for buy or sell pressure in the market. Fundamental analysis-research on determinants of stock value, such as earnings and dividends prospectus, expectations for future interest rates, and risk of the firm. Passive investment strategy-buying a well-diversified portfolio without attempting to search out mispriced securities. Index fund-a mutual fund holding shares in proportion to their representation in a market index such as the S&P. filter rule-a rule for buying of selling stock according to recent price movements. P/E effect-portfolios of low p/e stocks have exhibited higher average risk-adjusted returns than high p/e stocks. Small-firm effect-stocks of small firms have earned abnormal returns, primarily in the month of January. Neglected-firm affect-the tendency of investments in stock of less well-known firms to generate abnormal returns. Book-to-market effect-the tendency for investments in shares of firms with high ratios of book value to market value to generate abnormal returns. Reversal-effect-the tendency of poorly performing stocks and well-performing stocks in one period to experience reversals in the following period. Series Geometric Mean Arithmetic Mean Standard Deviation Distribution Small Company Stocks 12.46% 18.77% 39.95 ?------------? Large Company Stocks 11.01 13.00 20.33 ?---------? Long-term govt bonds 5.26 5.54 7.99 ?---? T-bills 3.75 3.80 3.31 ?? Inflation 3.08 3.18 4.49 ?--?
7:41:58 PM     comment []