8
Finance (Fach) / CAPM (Lektion)
<3
Diese Lektion wurde von Janaw55 erstellt.
Diese Lektion ist leider nicht zum lernen freigegeben.
- Definition Required Rate of Return & Cost of Capital Required Rate of Return Return required by investors to fund a project/firm with given risk characteristics. takes into account the risk of the project/firm as evaluated by investors. often we assume the project has the same risk of the firm undertaking it. Cost of Capital cost of raising funds from investors. equal to the “Required Rate of Return on the project/assets of the whole firm.’’ Risk Premium Shares are risky and shareholders are averse to risk Compensation for taking up additional risk. Risk as Standard Deviation in Returns Also known as monthly volatility Interpretation: "that value of portfolio can readily move up or down 5.56% in any month"
- Individual Shares vs. Stock Market: A Paradox? Diversified portfolios Relation between risk and return is very close to linear Individual stock RP is not closely related to its volatility. Standard deviation is NOT useful for measuring the risk of individual stocks, because they are not well diversified The component of risk that can be diversified away is not priced by the market
- The Importance of the Correlation Coefficient in the Two Assets PF Expected value is additive, but risk is not additive. (1) Perfect negative correlation gives perfect insurance, i.e. (Hedging) ρ = −1: Maximum benefits from diversification. You can get a zero risk PF (SP500 unbeatable cause of neg correlation) The expected return of a portfolio varies linearly with the portfolio weights The variance of the portfolio return does not vary linearly with portfolio weights This is why diversification reduces risk. The crucial parameter is the correlation coefficient. (2) Negative correlation: “If the correlation between two stocks is negative r < 0, when the first stock suffers negative returns, the second stock tends to give a positive return.” (2) Positive correlation: “If the correlation between two stocks is positive correl > 0, when the first stock goes up, the second stock tends to go up as well.” Example with ρ = +1: No benefits from diversification when p = 0, still some hedge
- The efficient frontier The set of portfolios that maximise expected return for a given level of std.
- Mean Variance Analyises Mean-variance analysis gives us a way to select a portfolio given expected returns, variances, and covariances. This does not tell us anything about what prices should be. Also, computing accurate expected returns is a tough problem because the confidence intervals on estimates are typically quite large. The CAPM is a model, based on the laws of supply and demand, of what the expected rate of return on an asset is.
- CAPM: Assumptions The following assumptions are used to derive the CAPM: Investors choose portfolios based on expected return and variance. All investors have identical estimates of the means, variances, and covariances of all assets. Investors trade in perfect capital markets (there are no frictions such as taxes, transaction costs, or restrictions on short sales / no differential between borrowing and lending rates)
- CAPM With borrowing/lending the efficient frontier is a straight line Investors Should hold a mix of only two assets: the risk-free asset & risky portfolio Hold these in different proportions, but the composition of the risky portfolio is the same for everybody. Since everyone holds the tangency portfolio, in equilibrium this must be the market portfolio (M). The risk of an individual asset i depends on the correlation of this asset’s return with the return on the market portfolio CAPM says that the expected return on an asset i should be proportional to the undiversifiable market risk, i.e., its Beta: In a market where investors can diversify by holding many assets in their portfolio, the risk premium is proportional to beta. The specific risk can be eliminated by holding diversified portfolios and is not priced
- Capital Market Line vs. Security Market Line Capital Market Line = Shows portfolios combining risk-free asset and efficient portfolio Shows highest return for each level of volatility Offers the best possible Risk-Return combination Only Invest in Asset with higest Sharpe Ratio if you can borrow and lend Security Market Line= Shows required Rate of Return for each securit as function of its beta with the market All stocks and portfolios should line on the SML Line through the risk-free investment and the market, Y Axis = Return, x-Axis = Beta
Anzeige