The power of compounding

aroominyork

Most people know the power of compounding but I've come across a great demonstration of it. Take a look at the prices of the Accumulation and Income versions of this equity income fund.

The Acc. fund grew by c.114% over five years while the Inc. fund grew c.64%. The difference is 50%, so you might think that translates into an average 10% dividend. Now look at the performance tables where the difference between the units represents the actual distribution: 6.29%, 5.62%, 5.46%, 6.73%, 5.95%, an average of 6.01%. The difference between 6.01% and 10% is the result of reinvesting the dividends in the Acc. fund and watching the growth compound. The quote attributed to Einstein is "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it."

El_Torro

For something to grow 50% in 5 years the growth rate would need to be 8.45% a year, not 10%.

i see your point though.

Altior

It's not really accurate. To be accurate, you'd need to add the income to the blue line.

masonic

You can work out the actual effect of compounding by looking at the difference between the two and back-calculating the yield. Using your figures compound income over 5 years = 50%.

A 50% annualised return would come from simple return of 8.45% per year, which, without compounding would amount to 8.45 * 5 = 42.3%, with an additional 7.7% coming from compounding to make the 50%. In other words compounding makes up around 15% of the additional returns of the acc fund vs if income were held in a separate cash account paying no interest.

The other way of doing it would be to add on the implied income as Altior suggests. This would reduce the difference to 20%, which is 17.5% of the overall return.

Mathematically, you can approximate the value of the wonder of compound interest using Euler's number e, since continuous compound interest can be calculated using r = e^i-1 where i is the decimal simple interest rate. Conversely the simple interest required to generate compound interest can be calculated using i = ln(r+1). For compound interest at 50%, i = ln(1.5) = 40.5%, which represents the theoretical maximum limit for the effect of compound interest of 19% of the total return for this level of return. Increase the underlying return and it will get better, and vice versa. Risk-based investments can exceed this limit when reinvestment takes place during a loss period, and subsequent compounding takes place during a growth period, but it is unlikely that you'd be able to achieve a persistent effect from that. Note that these figures are independent of time, due to continuous compounding the number of compounding periods is infinite.

That said, a 15-20% boost to returns is not to be sniffed at.

Alexland

aroominyork said:

The quote attributed to Einstein is "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it."

Einstein also said "When I'm dead you can quote me on anything"

where_are_we

The power of compounding becomes really significant over a long period of time. As mature investors it has helped our wealth accumulation from very meagre beginnings.  

Johnnyboy11

Worth pointing out that UK RPI was also enjoying the magic of compounding over those 5 years, up 38% in total, or about 6.7% annually. Until around 'Liberation Day' this year the Inc fund had barely made a real return for investors, ouch!

aroominyork

You live and learn... even about Euler's number.