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The duration of a stock is the average of the times until its cash flows are received, weighted by their present values. The most popular model of duration uses dividends as the cash flows. In vernacular, the duration of a stock is how long we need to receive dividends to be repaid the purchase price of the stock. If a stock doesn't pay dividends, other methods using distributable cash flows, may be utilized.
The duration of an equity is a noisy analogue of the Macaulay duration of a bond, due to the variability and unpredictability of dividend payments. The duration of a stock or the stock market is implied rather than deterministic.
Duration of the U.S. stock market as a whole, and most individual stocks within it, is many years to a few decades. A nominal value, assumed in many analyses, would be 20-30 years, analogous to long term bonds. Higher price/earnings and other multiples imply longer duration.
Duration is a measure of the price sensitivity of a stock to changes in the long term interest rate, i.e., the longer the duration, the more sensitive the stock is to interest rates.
In U.S. stock markets, an SEC rule adoption in 1982 (rule 10b-18) that allowed discretionary stock buybacks has distorted the calculation of duration based on dividends since at least the early 1990s. The rule change had no ascertainable impact on duration, but duration now needs to account for all cash distributions including buybacks.
The present value or value, i.e., the hypothetical fair price of a stock according to the Dividend Discount Model, is the sum of the present values of all its dividends in perpetuity. The simplest version of the model assumes constant growth, constant discount rate and constant dividend yield in perpetuity. Then the present value of the stock is
where
P is the price of the stock
D is the initial dividend amount
r is the periodic discount rate (either annual or quarterly)
g is the dividend growth rate (either annual or quarterly corresponding to r)
The requisite assumptions are hardly ever true in perpetuity, so the computed value is highly hypothetical.
In the Discounted Cash Flow Model (DCFM) of security analysis, the value of a security is the present value of all its future cash flows including interest or dividends and the implied cash flow of the residual value of the security itself, if any. A special case of the DCFM, based on a stock's dividend, is called the Dividend Discount Model. Under that model, the value of a stock depends on how long we expect to receive dividends, their cash amounts, spacing (usually monthly, quarterly or semiannually), and a hypothesized long term discount rate that incorporates inflation in the currency and risk on the firm's payouts. The duration of the stock is how long we need to receive dividends for the present value of the dividends plus the residual value of the stock to total to the price paid. Conceptually, it corresponds to the duration of a bond but the duration of a bond is deterministic and that of a stock is not. It is not necessary for the dividends to be reinvested – that's a separate risk, reinvestment risk, and does not affect the risks and therefore the value of the stock.
If a stock does not pay a dividend or pays a very low dividend, alternatively, analysts may use a firm's free cash flow taking into account any necessary capital expenditures, to approximate what distributable cash could be available to shareholders.
Low interest rates shorten duration because the present value of near term cash flows is relatively greater; high interest rates lengthen duration because we're more reliant on deeply discounted cash flows in the far future.
The duration of the U.S. stock market represented by the S&P 500 for example (or other broad index) as well as most individual stocks, is many years to several decades. Generally, higher price/earnings and other equity multiples imply longer duration and greater risk that the implied cash flows may not arrive as expected.
The first approximation, in years, to the duration of a stock is the ratio of the two terms, stock price divided by the annual dividend amount. Since the present value of future dividends gets a bit less with each passing year (or even quarter or month), the duration is a bit longer than that approximation. But the duration of a stock, unlike that of a bond, isn't deterministic. The stock price and dividend are taken directly from the market, and they're tangible. Everything else is hypothecated into the future: interest rates, growth, volatility, idiosyncratic risks, and dividend amounts. For European stocks, dividends aren't fixed, but paid as a proportion of profits, so even the base amounts 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.
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, what may be gained in mathematical precision is lost by the compounding of uncertainties, particularly about growth, over the term of 34 years: they make any numbers we may calculate with conjectural. It may be more appropriate to derive an empirical estimate of duration, and encapsulate it in a rule of thumb that's reasonable most of the time.
The price sensitivity of a stock versus duration, often called modified duration, is the percentage change in price in response to a 1% change in the long-term return that the stock is priced to deliver. The modified duration is duration divided by (1 + growth rate). There is some ambiguity in the literature when referring to duration; much of the time modified duration is referred to simply as "duration", and they have similar values, so much confusion results.
The modified duration formula assumes a linear relationship between percent change in return and percent change in price; but because returns compound, it overestimates the actual change in price. This difference is called "convexity".
In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.
In finance, a bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor. The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. The interest is usually payable at fixed intervals: semiannual, annual, and less often at other periods. Thus, a bond is a form of loan or IOU. Bonds provide the borrower with external funds to finance long-term investments or, in the case of government bonds, to finance current expenditure.
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.
In finance, a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence. For example, the United Kingdom (UK) government issued them in the past; these were known as consols and were all finally redeemed in 2015.
In finance, a convertible bond, convertible note, or convertible debt is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value. It is a hybrid security with debt- and equity-like features. It originated in the mid-19th century, and was used by early speculators such as Jacob Little and Daniel Drew to counter market cornering.
Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the principal amount on maturity. Fixed-income securities can be contrasted with equity securities that create no obligation to pay dividends or any other form of income. Bonds carry a level of legal protections for investors that equity securities do not: in the event of a bankruptcy, bond holders would be repaid after liquidation of assets, whereas shareholders with stock often receive nothing.
Stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will overall rise in value, while overvalued stocks will generally decrease in value. A target price is a price at which an analyst believes a stock to be fairly valued relative to its projected and historical earnings.
In economics and accounting, the cost of capital is the cost of a company's funds, or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.
Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
Business valuation is a process and a set of procedures used to estimate the economic value of an owner's interest in a business. Here various valuation techniques are used by financial market participants to determine the price they are willing to pay or receive to effect a sale of the business. In addition to estimating the selling price of a business, the same valuation tools are often used by business appraisers to resolve disputes related to estate and gift taxation, divorce litigation, allocate business purchase price among business assets, establish a formula for estimating the value of partners' ownership interest for buy-sell agreements, and many other business and legal purposes such as in shareholders deadlock, divorce litigation and estate contest.
The "Fed model", or "Fed Stock Valuation Model" (FSVM), is a disputed theory of equity valuation that compares the stock market's forward earnings yield to the nominal yield on long-term government bonds, and that the stock market – as a whole – is fairly valued, when the one-year forward-looking I/B/E/S earnings yield equals the 10-year nominal Treasury yield; deviations suggest over-or-under valuation.
Valuation using discounted cash flows is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money. The cash flows are made up of those within the “explicit” forecast period, together with a continuing or terminal value that represents the cash flow stream after the forecast period. In several contexts, DCF valuation is referred to as the "income approach".
The following outline is provided as an overview of and topical guide to finance:
The income approach is a real estate appraisal valuation method. It is one of three major groups of methodologies, called valuation approaches, used by appraisers. It is particularly common in commercial real estate appraisal and in business appraisal. The fundamental math is similar to the methods used for financial valuation, securities analysis, or bond pricing. However, there are some significant and important modifications when used in real estate or business valuation.
Earnings growth is the annual compound annual growth rate (CAGR) of earnings from investments.
In financial economics, the dividend discount model (DDM) is a method of valuing the price of a company's capital stock or business value based on the assertion that intrinsic value is determined by the sum of future cash flows from dividend payments to shareholders, discounted back to their present value. The constant-growth form of the DDM is sometimes referred to as the Gordon growth model (GGM), after Myron J. Gordon of the Massachusetts Institute of Technology, the University of Rochester, and the University of Toronto, who published it along with Eli Shapiro in 1956 and made reference to it in 1959. Their work borrowed heavily from the theoretical and mathematical ideas found in John Burr Williams 1938 book "The Theory of Investment Value," which put forth the dividend discount model 18 years before Gordon and Shapiro.
Dividend policy, in financial management and corporate finance, is concerned with the policies regarding dividends; more specifically paying a cash dividend in the present, as opposed to, presumably, paying an increased dividend at a later stage. Practical and theoretical considerations will inform this thinking.
Corporate finance is the area of finance that deals with the sources of funding, and the capital structure of businesses, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value.