Question

Analysts who research the stock market have found differences in required rates of return based on company size. The economist Eugene Fama studied stock market returns for all stocks from 1927 to 2011. Dividing the market up into deciles by market capitalization – from the largest 10% of companies to the smallest 10% of “micro-caps” – Dr. Fama found that the largest stocks returned 10.9% while the lowest group returned 21.6%. There was a continuum such that each smaller decile showed a higher rate of return. Average returns for the smallest half of the market were 17.24% vs. 13.32% for the larger half. Using these numbers for historical rates of return and the rule of 72, calculate the returns for a portfolio of $100,000 invested in small cap stocks vs. a portfolio of large caps – over a period of 30 years.

Answer 1

Years Require to Double Your Investment Under given Interest rate N = 72/ i (i = Annual Return)

No of compounding can be done in 30 Years C = 30/ N

Return Factor X = 2C

Portfolio Futue Value= 10,000 *X

Return of Portfolio (In percentage)= (10,000 *X - 10,000)*100/ 10,000 = (X - 1)*100

Invested in Large Cap (Largest 10% of companies)

Annual Return = 10.9%

Years Require to Double Your Investment Under given Interest rate N = 72/ 10.9 = 6.605

No of compounding can be done in 30 Years C = 30/ N = 30/ 6.605 = 4.5417

Return Factor = 2^4.5417 = 23.2909

Future Value = (23.2909 - 1) * 100 = 2229%

Invested in Small Cap ( Bottom 50% of companies)

Annual Return = 17.24%

Years Require to Double Your Investment Under given Interest rate N = 72/ 17.24 = 4.1763

No of compounding can be done in 30 Years C = 30/ N = 7.18333

Return Factor = 2^7.18333 = 145.34457

Future Value = (145.34457 - 1) * 100 = 14434%

Invested in Micro Cap (Bottom 50% of companies)

Annual Return = 13.32%

Years Require to Double Your Investment Under given Interest rate  N = 72/ 13.32 = 5.4054

No of compounding can be done in 30 Years  C =  30/ 5.4054 = 5.55

Return Factor = 2^5.55 = 46.85074

Future Value = (46.85074- 1) * 100 = 4585%

Invested in Micro Cap (Bottom10% of companies)

Annual Return = 21.6%

Years Require to Double Your Investment Under given Interest rate N = 72/ 21.60 = 3.333

No of compounding can be done in 30 Years C = 30/ 3.3333  = 9

Return Factor = 2^9 = 512

Future Value = (512 - 1) * 100 = 51100%