FIN 310 1st EditionFinal Exam Study Guide Arithmetic vs Geometric Average ReturnsArithmetic: - The sum of returns in each period divided by the number of periods- Statistic ignores compounding - Does not represent and equivalent, single quarterly rate for the year- Without information beyond the historical sample, arithmetic average is the best to forecast performance for the next quarter Geometric: - The single per-period return that gives the same cumulative performance as the sequence- Also called time-weighted return because it ignores quarter to quarter variation in funds under management Arithmetic is simply the sum of the quarterly returns divided by the number of the quarters while the geometric is calculated by compounding the actual period-by- period returns and then finding the per-period rate that will compound to the same final valueNominal vs. Real Rates of InterestNominal Interest: - The Interest rate in terms of nominal, not adjusted for purchasing power- Nominal is the growth rate of money itself- Nominal = real interest + loss of purchasing power (inflation)Real Interest: - The excess of the interest rate over the inflation rate- The growth rate of purchasing power derived from an investment- Real interest = nominal- loss of purchasing power(inflation)Factors that Affect Interest Rates:- Supply-households- Demand-business’s- Government’s Net Supply and/or Demand- Federal Reserve ActionsYield CurveYield curve: A graph of yield to maturity as a function of term to maturity- Also called term structure of interest because it relates yields to maturity to the term of each bond (yield vs. yield to maturity)- Published regularly and found in The Wall Street JournalTheories of term structure of interestExpectations Theory: theory that yields to maturity are determined solely by the expectations of future short-term interest ratesLiquidity Preference Theory: the theory that investors demand a risk premium on long-term bondsMarket Segmentation Theory: addressed supply and demand or certain maturity sectors and determines interest rates for those sectors. It can explain almost every type of yield curve an investor can find. Basically means that trading in the distinct segments determines the various rates. Subjective Returns and Standard DeviationSubjective Returns=∑ psrsp(s) = probability of a stater(s) = return if a state occursStandard Deviation=[variance]1/2Var= ∑(ps)x(rs-E(r))^2Utility Maximization and ScoresUtility:Based on the expected return and risk of a portfolio, can be used as a means of ranking portfoliosUtility Score:U = E ( r ) - .005 A s 2A measures the level of risk aversionTypes of RiskSystematic: remains even when there is diversification, some factors are business cycle, inflation, and interest ratesUnsystematic: Firm specific, eliminated through diversificationTotal Risk= Systematic + UnsystematicLevel of Risk Aversion -Investors level of Risk Aversion has a big impact on the types of assets they will choose-Price of Asset must be proportional to level of risk for an investorCapital Allocation Line: plot of risk-return combinations available by varying portfolio allocation between a risk-free asset and a risky portfolioDominance PrincipleDominance Principle: A dominates B if E(rA) > E(rB) AND σA < σB Investors will prefer A over B if it has a higher mean return and a lower variance or standard deviation, stock will dominate another stock because these criteria lead to higher expected return and lower volatilityCorrelation and Covariance-key determinant for portfolio risk is determining the extent in which two assets vary either in tandem or opposition-portfolio risk depends on covariance between the returns of the assets in the portfolioCovariance:COV (rA , rB ) = ∑Pr(s)[rA (s) – E(rA)] [rB (s) – E(rB)]Correlation Coefficient: is a pure number range from values of -1 to 1; a correlation coefficient of -1 means that one asset’s return is perfectly inverse with the othersρ(A,B) = COV (rA , rB ) / σAσBOptimal Risky Portfolio -The best combination of risky assets to be mixed with safe assets to form the complete portfolioReturn on Portfolio: The rate of return on a portfolio is a weighted average of the rates of returnof each asset comprising the portfolio, with the portfolio proportions as weightsrp = W1r1 + W2r2W1 = Proportion of funds in Security 1W2 = Proportion of funds in Security 2r1 = Expected return on Security 1r2 = Expected return on Security 2Portfolio Risk: When two risky assets with variances s12 and s22, respectively, are combined into aportfolio with portfolio weights w1 and w2, respectively, the portfolio variance is given by:sp2 = w12s12 + w22s22 + 2W1W2 Cov(r1r2)Asset AllocationDiversification: Investments are made in a wide variety of assets so that exposure to the risk of any particular security is limited-An Investors personal risk drives asset allocation-Risk must be outweighed by return according to level of risk aversionPortfolio Risk with risk-free Asset-When a risky asset is combined with a risk-free asset, the portfolio standard deviation equals the risky asset’s standard deviation multiplied by the portfolio proportion invested in the risky assetσp=wriskyasset×