Quantitative and Economics Flashcards
Use linear equation to forecast results one quarter ahead
Salest=Bo + B1t + et
- Analysis done over 15 years
- Intercept coefficient 10
- Trend coefficient 16
- Time variable (quarter #) t
Yt = 10 + 16(61) = 986
- Remember you are forecasting out an additional quarter plus the 60 quarters already studied.
Sample covariance (cov)
∑(x-xbar)(y-ybar) / n-1
Sample correlation coefficient (r)
Cov(x,y) / (Sx)(Sy)S = Standard Deviation
Limitations of Correlation Analysis
- Linear relationships (not quadratic)2. Outliers (news vs. noise)3. Not causation4. Spurious (Chance, mixed third variables)
Two-tailed “t-test” with n-2 degrees of freedom to tell if population correlation is 0 or not 0
t = r√n-2 / √1-r^2
Decision rule for two-tailed test
Reject H0 if1. t-stat > +ve tc (Positive critical value)2. t-stat < -ve tc (Negative critical value)3. t-stat > |Tc||Tc| = T critical value
Dependent Variable (which axis and description)
- Y-axis2. Seeking to explain or predict the Y variable
Independent Variable (which axis and description)
- X-axis2. Used to explain or predict the Y or dependent variable
Regression Model Equation
Yi = b0 + b1Xi+Ei1. i = 1,…,n2. This uses the estimates of Y (includes a carot above the Y and b)
Some of Squared Errors (SSE)
∑(Yi - Yi~ or (b0+b1Xi))^2
Calculation for b1
b1 = Cov(X,Y) / Var (X)
Calculation for b0
b0 = Yaverage - b1(Xaverage)
The midpoint of a regression series
= (Xbar, Ybar)1. will be plotted on the regression line
Standard Deviation
NAME?
Steps for calculating correlation coefficient
- calculate sum and mean of each variable2. Calculate cross product of (xi-xbar)(yi-ybar) for each variable (by row)3. Calculate squared deviation for each variable (by row)
Regression Line Equation
Yi~ = b0~+b1~Xi~ = ‘hat’ or estimate of these variables
Find correlation of two stocks using market model
Calcuate total risk (standard deviation) for both securities being compared. V’ is the common macro factor variance:Security 1 σ² = (β² x V’) + unsystematic risk²Calculate covariance:Beta(a) X Beta(b) X common macro factor varianceCalculate correlation: cov/totalriskA X total risk Y
Calculate a Cross Rate
Cross Rate = (F/USD) / (D/USD)
- Imagine that “usd” is a common denominator
Relative Purchasing Power Parity
ES1 = So X [(1+inflationF)^2 / (1+inflationD)^2]
International Fisher Relation (determine if projected inflation rates are consistent)
(1+rF%USD)/(1+rF%F) = 1+expectedinfUSD/1+infF = should equal exp infF
(1+rF%D)/(1+rF%USD) = 1+infD / 1+expinfUSD = should equal exp infD
Uncovered Interest Rate Parity Forecast
So[(1+rF%D)/(1+rF%F)] = Uncovered Interest Rate Parity Forecast
This is also how to calculate a no-arbitrage forward rate value.
DON’T FORGET TO BREAK THE RISK FREE RATE OUT BY THE TIME/360
Mundell Flemming Model (expansionary Monetary Policy and Fiscal Policy)
Expansionary Monetary Policy
- Flexible exchange rates: lower interest rates and currency drops
- Fixed exchange rates: expansionary policy is futile and limited to FX reserves
Expansionary Fiscal Policy
- Flexible exchange rates: increases inflation&interest rates driving currency higher
- Fixed exchange rates: To prevent currency appreciation currency will be sold and increase money supply
Average Cov of port approaches total average Cov when…
The number of assets in the portfolio are large.
Minimum Variance Portfolio
Portfolio that has the smallest variance among portfolios with identical expected returns.