claim: ( Multiplying .95 by itself 15 times yields 46.3 percent. )”
evidence: Assuming returns are reinvested, if the returns over n { \displaystyle n } successive time sub-periods are R 1 , R 2 , R 3 , ⋯ , R n { \displaystyle R { 1 },R { 2 },R { 3 },\cdots ,R { n } } , then the cumulative return or overall return over the overall time period is the result of compounding the returns together : (  1 + R 1  ) (  1 + R 2  ) ⋯ (  1 + R n  ) − 1 { \displaystyle ( 1+R { 1 } )( 1+R { 2 } )\cdots ( 1+R { n } )-1 } If the returns are logarithmic returns however, the logarithmic return over the overall time period is : ∑ i = 1 n R l o g , i = R l o g , 1 + R l o g , 2 + R l o g , 3 + ⋯ + R l o g , n { \displaystyle \sum  { i=1 }^{ n }R { \mathrm { log } ,i }=R { \mathrm { log } ,1 }+R { \mathrm { log } ,2 }+R { \mathrm { log } ,3 }+\cdots +R { \mathrm { log } ,n } } This formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e.