are hypothecated. Historically, before the 1990s, the average dividend yield on U.S. stocks had been a little less than 4%, so the first approximation to duration has been a little more than 25 years. The hypothecated duration taking into account changes in the present value of future dividends, has been about 33% longer, which gives a duration in the low 30s (years), Traditionally, analysts have cited the duration of the U.S. market as 20-30 years. Since the last recession in 2008-09, multiples have become inflated and dividend yields have dropped, so the current implied duration of stocks according to the Dividend Discount Model (DDM) has risen to at least 80 years (Dec. 2021). However, the implied duration from other means isn't nearly that long. A one-stage mathematical model using current growth, etc, is usually not sustainable, i.e. those conditions aren't expected to obtain for possibly decades. Therefore, most analysts use a 2-stage or 3-stage model to assess present value and duration of stocks. It is improbable that stock duration can reasonably exceed a person's working and investing career of 45-50 years. Since duration and present value (or just value) of a stock are terms in the same equation, which can be solved for one by making assumptions about the other, an excessively long duration can provide a check on over enthusiastic stock valuations. Example Suppose a stock costing $100 pays a 4% dividend, grows at a terminal rate of 6.5% and has a discount rate of 7.9%. The price/dividend first estimate of 25 years is easily calculated. If we assume an additional 33% duration to account for the discounted value of future dividend payments, that yields a duration of 33.3 years. Present value of the dividend payment in year one is $4, year two $4*1.065*.921=$3.92, year three $3.85, etc. There is an infinite series, such that each year's dividend payment has a present value of .9809 of the previous year's payment, starting with $4. The present value of the stock in perpetuity (i.e. the sum of present values of all dividend payments) is $209.04. To recover the price paid of $100 must take some time considerably less than till the end of time. That time is between 33 and 34 years: the present value of dividends paid through the 34th year (but not the 33rd) will exceed $100. That is very close to the rule of thumb estimate above. However,