Financial

Fundamentals

Average Return

Rt,t+1=Pt+1PtPtR_{t,t+1} = {P_{t+1}-P_t \over P_t}

Average return is misleading because it disregards volatility.

Logarithmic Return

Often used because percentages can get very small.

rt=log(1+Rt)=logPtPt1=logPtlogPt1r_t = log(1+R_t) = log{ P_t \over P_{t-1}} = log P_t - log P_{t-1}

Compounded Return

Rt,t+2=(1+Rt,t+1)(1+Rt+1,t+2)1R_{t,t+2} = (1+R_{t,t+1})(1+R_{t+1,t+2})-1

We can get the annualized returns by repeating this for every monthly return.