Here is a stock market quiz regarding the Dow Jones Industrial Average (DJIA) closing above 19,000. I think most people will be surprised @ the result of the quiz – including the many investors in the readership.
Stock Market Quiz:
The table below shows the dates of each of the nineteen 1,000 point incremental milestones reached by the DJIA, starting with 1,000 in November 1972 through 19,000 last month.
What is the real (inflation adjusted) compound annual rate of return from November 1972 to November 2016 for the DJIA given a compound annual inflation rate of 4.04% during this time? Do not consider broker fees, dividends, taxes, timing regarding the payment of taxes, or slippage between the expected price of a trade & the price @ which the trade is actually executed.
I will post all correct answers or alternatively will send the solution privately to anyone who requests it if no one figures it out.
click on graphic to enlarge
Dear RTE,
ReplyDeleteI am unable to do the math to determine the real rate of return; however, I would imagine that the number is about zero. The USA went off the gold standard in 1971 and from everything I read now real incomes for men have not changed very much since that time. So the DJIA may be a high number but real returns on investment are not that much different than they were in the late 1960s-1972.
I will look at the math answer when you publish it. If no one answers correctly please send me the answer.
My figure is subtracting inflation of 4.04%, (2.3%)
ReplyDeletePlease explain more? How did you get the number to subtract 4.04% from?
DeleteTook the average of returned dividends and interest.
DeleteIs the average of returned dividends & interest 6.34% - meaning 6.34 – 4.04 = 2.3 real compound annual rate of return?
DeleteYes, that is all I used.
DeletePlease work the quiz again using only the DJIA of 1,000 to 19,000. The directions said to not consider dividends. Your answer is very close though.
DeleteI don't fully understand the question but if he is looking for the annual interest rate it would be 6.77%...but if he is looking for it adjusted for inflation my guess would be 6.77% minus the 4.04% which leaves 2.73%
ReplyDeletePlease provide some methodology. I have another person who worked it wrong but got pretty close to the right answer. Confirm I am looking for the total rate minus inflation – which is the real rate of return. I think you have it.
DeleteI just plugged in the numbers to a calculator and started at 10% to see where it left me....then adjusted the rate to get to the right numbers and settled on 6.77%. Then deducted the 4.04% inflation to get to 2.73....i know it isn't the most efficient way to do it...but I got there in about 15 - 20 mins
DeleteCongrats HowK - you used trial & error which is fine. The other method uses logarithms.
DeleteMy Solution:
The period in question is 44 years from November 1972 to November 2016. The total rate of return for the DJIA to go from 1,000 to 19,000 (i.e., 19 times higher) in 44 years can be determined by using the compound-interest law & solving the following equation where x = the compound interest factor in the form (1+ i) where i is the total compound annual rate of return.
(x)44 = 19
solve for x taking logarithms of each side or simply by trial & error
x = 1.0693 meaning that 6.93% is the total compound annual rate of return
Since we know that the compound annual inflation rate is given as 4.04% we can determine by subtraction (6.93 – 4.04) that the real compound annual rate of return over the 44 years is 2.89%.
Alternate solution:
We know the compound annual inflation rate is 4.04%. Therefore (1.0404)44 = 5.71 We are trying to determine the % return so 19/5.71 = 3.33 – i.e., 19,000 is 3.33 times higher (233% compound annual return) than 5,710.
(x)44 = 3.33
x = 1.0278 meaning that 2.78% is the real compound annual rate of return
Good agreement between the two methods of 2.89% & 2.78%
Thanks for the solution, never would have figured it out this way.
DeleteAs for me, this is above my pay grade!
ReplyDelete