Quant is easily one of the WORSt sections in my opinion…
Going over misspecificaitons in multiple regression. Can someone please explain this line?
“Regression assuems that the dependent variable is linearly related to each of the independent variables. Typically, however, market capitalization is not linearly related to portfolio reutrns, but the natural log of market cap is linearly related.”
Hmm… LN on the calculator, i thouhgt was the calculator symbol that had to be used for calculatating compounded infinity E^x
Basically when you take the natural log it resembles a more linear relationship. I won’t delve into the maths but if you try this in excel you can see what I mean.
In one column create an exponential series, e.g. 100 growing by 10% each time (so start with 100 in the first cell then starting the next row down multiply each previous cell by 1.10, do this each row down for ten rows). Then in the column next to it, take the natural log of the number to its left and copy the formula down ten rows. You will see that this log series now grows at a linear rate unlike the exponential growth in the original series.
The natural logarithm function “undoes” the exponential (to the base e) function: if y = e^x, then x = ln(y).
Thus, in applications where you think that something (the value of a portfolio, say) is growing at a (nearly) constant growth rate, the plot of that value versus, say, time, will be (close to) an exponential curve, but the plot of ln(value) will be (close to) a straight line.