Articles Flashcards
CAPM Theory
advantages of Arithmetic average return
- Represents the mean of all the returns that may possibly occur over the investment holding period
- Best estimator of expected (short-term) future returns
- The best gauge of the expected risk premium
CAPM Theory
advantages of geometric average return
- when past performance is being considered, the geometric mean (rg) summarizes the annualized rate of return over historical period;
- Best measure of realized (past) returns on an investment;
CAPM Theory
Effective Annual Rate - formula
EAR = (1+APR/K)^K-1
CAPM Theory
Describe relation between risk and realized return
The more risky asset is (higher volatility (st. dev.)), the higher realized returns
CAPM Theory
Conclusions for historical volatility and returns for individual stocks
- Relationship between size and risk: large stocks have lower volatility
- Even largest stocks more volatile than S&P
- No clear relationship between volatility and return
- Volatility doesn’t explain returns for individual stocks
CAPM Theory
Equity risk premium
the difference between the return on equities and the return on a risk-free asset
CAPM Theory
Inverse relation between risk premium and price
Risky assets have relatively low price, but a relatively higher expected return
CAPM Theory
The risk premium matters because it is central to:
- Projecting future investment returns - allocation of portfolio investment
- Calculating a company’s cost of equity capital - Determine the appropriate risk adjusted discount rate
- Valuing companies and shares - Discount future cash flow
- Appraising investment projects
- Determining fair rates of return for regulated utilities
CAPM Theory
Market risk premium - formula
Rm-Rf
CAPM Theory
Constant-growth model Formula
PV = DIV1/(r-g)
CAPM Theory
Relation between price and risk
Higher PV implies less risk - inverse relation between price and risk
CAPM Theory
Standard deviation formula and explanation
St.Dev = SQRT(Variance)
This is our measure of risk - volatility
Measured in percent - the same dimension as we gauge returns;
CAPM Theory
Coefficient of correlation formula
corr = (Cov AB)/(St.Dev. A * St. Dev B)
CAPM Theory
The sense of correlation
Correlation measures how returns move in relation to each other
CAPM Theory
Variance of portfolio returns - formula
Variance P = (wa)^2Var a + (wb)^2Var b + 2*(wa * wb * Cor ab * st. dev a * st. dev b)
CAPM Theory
Skewness - this is
A measure of symmetry, or more precisely, the lack of symmetry
CAPM Theory
Kurtosis - this is
A measure of whether the data are peaked or flat relative to a normal distribution
CAPM Theory
Skewness formula
Skewness = ([nju]^3/(st. dev)^3)
[nju]^3 - third moment - asymmetry measure
CAPM Theory
Valuation of skewness
Skewness for a normal distribution is zero, and any symmetric data should have a skewness near zero
- Negative values for skewness indicate data that skewed left
- Positive values for skewness indicate data that skewed right
CAPM Theory
Kurtosis (formula)
Kurtosis = ([nju]^4/(st. dev)^4)-3
[nju]^4 - fourth moment - asymmetry measure
CAPM Theory
Kurtosis valuation
The kurtosis for a standard normal distribution is 3
*for this reason, excess kurtosis is defined so that the standard normal distribution has a kurtosis of K=0
- Positive kurtosis indicates a “peaked” distribution;
- Negative kurtosis indicates a “flat” distribution
CAPM Theory
contribution of covariance
Covariance is the contribution of the security to the variance of the well diversified portfolio
CAPM Theory Leptokurtic distribution (definition)
A distribution with wide tails and a narrow peak (K>3)
CAPM Theory
Platykurtic ditribution
A distribution with thin tails and a relatively flat middle (K
CAPM Theory
Advantages of Leptokurtic returns
Returns series that are characterized by jumps as opposed to more continuous changes will tend to be leptocurtic
- Low probability of extreme outcomes;
- Regulatory process dampens moderately deviant returns, forcing them closer to the mean
CAPM Theory
Expected portfolio return formula
RE= w1r1+w2r2
CAPM Theory
Draw co-variance matrix for two assets
http://cmacfm.mazoo.net/WindowsLiveWriter/9cbcdc0f2b05_DB21/almost-covariance-matrix%5B4%5D.gif
CAPM Theory
How many assets are necessary for diversification
the gain from diversification comes fast and tapers off relatively fast 10-15 assets enough to capture the major gains from diversification
CAPM Theory
Why portfolio variance equals average covariance
- gauges the systematic risk that affects all assets
* Unique risk (individual variance) diversified away
CAPM Theory
Diversification -
Strategy designed to reduce risk by spreading the portfolio across many investments
CAPM Theory
Unique risk
Risk factor affecting only that firm
CAPM Theory
Market risk
Economy-wide sources of risk that affect the overall stock market
CAPM Theory
Beta - definition
Marginal contribution to portfolio risk.
The beta of an individual security measures in sensitivity to market movements
CAPM Theory
Beta - formula
Bim=(Covarince im)/Variance m
CAPM Theory
Beta’s valuation
Brf = 0
Bm = 1 - market portfolio perfectly correlated with itself
*Stocks with betas greater than 1 tend to amplify the overall movements of the market;
*Stocks with betas between 0 and 1 tend to move in the same direction as market, but not as far
CAPM Theory
Inverse relation between price and risk
the larger the systematic risk is, the lower is the price of the asset
CAPM Theory
two implications from diversification
- only systematic risk determines expected returns
2. Value additivity - Investors that can diversify on their own account will not pay extra for firms that diversify.
CAPM Theory
Ranking by Mean Variance criterion (the matrix)
C:\Users\Admin\Documents\Petrovics\sse\sse\Year 2\FE\Ranking by MV Criterion.JPG
CAPM Theory
the portfolio opportunity set
http://analystnotes.com/graph/portfolio/SS12SBsubd1.gif
CAPM Theory
Minimum Variance Portfolio (Formula)
Xmin(S) = http://images.slideplayer.com/9/2576471/slides/slide_21.jpg
CAPM Theory
Describe simply process for short selling
Borrow a stock, sell it to cash in and then restore it to the original owner by buying back.
CAPM Theory
Two fund separation theorem
Assumptions:
Homogeneous expectations
Same lending and borrowing rate for all investors
Theorem:
Each investor will choose the same combination of risky assets. The optimal combination of risky assets for any investor can be determined without any knowledge about the investors preference toward risk and return.
CORP.FIN.
Types of dividends
Regular d.
Special d. (regular + bonus)
Stock split d. (pay dividends as shares)
Liquidating d. (sell assets - then pay)
CORP.FIN.
Types of share repurchases
Open market repurchase (95% of all rep.) Tender offer (an offer to all s/h to buy back a specified amount of shares at a specified price) Dutch auction (a share repurchase method as an auction) Targeted repurchase (direct negotiation with major s/h)
CORP.FIN.
MM (1961) dividend irrelevance proposition
In perfect capital markets, holding fixed the investment
policy of a firm, the firm’s choice of dividend policy is
irrelevant and does not affect the initial share price (or
shareholder wealth).
i.e., investors are indifferent between:
1. Free cash flow being paid out as a dividend
2. Free cash flow being used to repurchase shares
3. Shares being issued to pay a dividend larger than free cash
flows
CORP.FIN.
ROE>
ROE Negative NPV projects -> pay higher div. to increase company value;
ROE>r(e) -> Positive NPV projects -> pay less div. (reinvest more) to increase company value;
CORP.FIN.
Explain lifecycle theory
Young firms: a lot of profitable investment opportunities (i.e. NPV>0) and a need for financing -> pay more in dividends.
Mature firms: sufficient earnings to finance future projects, fewer profitable investment opportunities-> pay more in dividends
CORP.FIN.
DeAngelo (2008) Proposition
DeAngelo argues that empirical evidence is most consistent between agency costs and capital raising costs:
-To pay dividends -> increases probability of needing to raise capital ->raising capital is costly (particularly due to valuation uncertainty and adverse selection) -> ‘wasted’ value
- Not paying dividends -> increases retained earnings ->
increases agency costs (misappropriation, intentional or
unintentional behavioural biases) -> ‘wasted’ value
CORP.FIN. (CORPORATE PAYOUT POLICY + lecture slides)
Reasons for low dividend (5)
Reasons for high dividend (4)
Reasons for low dividends
1) Good investment prospects (positive NPV), as you have more retained earnings left;
2) Personal taxes (dividends are more costly than capital gains);
3) Costs of financial distress (it is better to sit on cash, than deal with fin. distress due to defaulting on debts)
4) High issuance costs (equity issue is costly, so it is better to sit on cash)
5) Clientele effect (for each person it is individual how much is it taxed on the div or capital gains)
Reasons for high dividends
1) lack of good investment prospects (only zero/negative NPV projects available), e.g. mature firms;
2) Information assymetry (dividends signal firm’s future performance);
3) to lower agency costs (less is left for managers)
4) Bird in hand theory (лучше синица в руке, чем журавль в небе - if highly uncertain investments, better to pay out as div)
5) Clientele effect (for each person it is individual how much is it taxed on the div or capital gains);
CORP.FIN.
What capital structure will maximize the value of the firm?
MM Proposition
Modigliani and Miller’s answer is that under a set of
conditions this question is irrelevant because capital
structure does not affect the value of a firm.
In a perfect capital market, the total value of a firm is
equal to the market value of the total cash flows
generated by its assets and is not affected by its choice
of capital structure.
