Duff and Phelps $(2022$SBBI Yearbook$)$ report that an investment of $$1$ in

Small Cap Stocks, made at the beginning of $1926$ grew to $$56,033\mathrm{.}70($nom$-$

inal dollars $-$ not inflation adjusted$)$ at year end, $2021.$ This is a period of $96$

years. Their calculations assume no transactions costs or taxes and all divi$-$

dends and capital gains are reinvested $-$ there is NO withdrawal of capital for

consumption during the $96$ years accumulation period.

Your problem is to use this information to compute or to find the geometric,

or compound annual return, on this $$1$ investment made in $1926.$ Clearly

state any formula used to compute or find the geometric return, denoted by $R_G.$

Be sure to show your work for full credit on this question.

Briefly discuss the use of the geometric or compound returns in assessing

overall market returns performance. For example, why use the geometric rather

than time averaged returns to market portfolios as an index of portfolio per$-$

formance $($comparing alternative portfolio historical observed outcomes from an

investor's vantage$).$