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Let $P_t$ be the price of the overall market index at the end of quarter $t$ Let $D_t$ be the dividend for the overall market in quarter $t$ Let $X_t = \frac{D_t}{P_t}$ be the dividend to price ratio. Two key concepts in time-series statistics are stationarity and ergodicity. If the dividends to price ratio is a stationary, ergodic process, then dividend ...

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Maybe I am a little bit late to the party, but I want to give a shot. As in Campbell and Shiller, start from the identity $R_{t+1}\equiv\frac{P_{t+1}+D_{t+1}}{P_t}$ where $R_{t+1}$ is the gross return between time $t$ and $t+1$, and $P_t$ is the price at time $t$. Rearrange the relationship as $R_{t+1} =\frac{D_{t+1}}{D_t}\frac{\left(1+\frac{P_{t+1}}{D_{t+1}}... 8 Basically the Total Return Index assumes reinvestments compared to "regular" indices. "A total return index is an index that measures the performance of a group of components by assuming that all cash distributions are reinvested, in addition to tracking the components' price movements.1 While it is common to refer to equity based indices, there ... 6 You could compute index dividend yield from ATM options using linearized put-call parity (assuming index options are European.) The present value of the dividend payment is:$PV(div) = P - C + (S - K) + K(e^{rT} - 1)$where$r$is interest rate to the option expiration and$T$is time to maturity in years. Then the implied dividend is:$d = \frac{PV(div)}{...

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There are 2 ways to do it. The good-enough way, and the complete and complex way. The Good-Enough Way Here you will convert to a situation where you can apply put-call parity. Begin by finding the strike $K$ where put and call prices are closest to each other. This might not end up being the closest-to-the-money strike, but it will do. Now run the ...

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I'm not sure how deep of a question you are asking. The dog that did not bark is from a Sherlock Holmes murder mystery. The dog at the house did not bark at the intruder, so Holmes believed the dog knew the intruder. Therefore, the lack of evidence like barking, was itself the evidence. In the Chochrane paper, the introduction mentions that the lack of ...

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If you assume that dividends are discrete but proportional to the pre dividend date stock price then the BS formula is exact provided you correctly compute the expiry date stock forward price, hence the continuous dividend yield case calibrated to the correct forward will give the correct result (this is because with proportional dividends, discrete or ...

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Vanguard S&P 500 index fund tracks the index and not the total return because it pays dividends out to the owners of the fund... some investors reinvest the dividends, some investors spend their dividends, etc., so, because they cannot control the reinvestment and distribute the dividends, they benchmark against the S&P 500 index and not the total ...

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If you assume the same tax rate $\alpha$ for all shareholders, then out of a dividend $D$ the amount $\alpha D$ goes to the government and the amount $(1-\alpha) D$ goes to the shareholders. In a theoretical pure no arbitrage environment, and assuming no interest rate discounting for the sake of simplicity, this would imply that the stock price would go down ...

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The paper is generally correct, but it is not a general statement, as in a general truth of options hedging in a theoretical context, rather a statement regarding how the structured derivs market is typically set up: retail and institutional investors buy a large number of products that at their core entail the dealer buying (from the investor) long-dated (...

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It is indeed no rounding error, but follows from the way Yahoo computes the adjusted price: it does not reflect the actual returns of the investor. Just look at August 17 and 20. The actual close prices were 10.75 and 9.95. On August 20 the company went ex-dividend for an amount 0.4508. The return on that day is $\frac{P_t+D_t}{P_{t-1}} -1 = \frac{9.95+0.... 3 What do you mean by annotation date, there is a declaration(announcement) date, ex-date, record date but I've never heard of an annotation date. Dividends are not decided always at the fiscal year end, in some countries they are approved by the shareholders general meeting which can happen at any time during the year, some companies pay quarterly, others ... 3 You get nothing, by this logic you could accumulate risk-free money all day by buying/selling on the ex-date as long as the dividend is larger than the spread. 3 I would have put this in a comment, but it was too long. I wouldn't really classify it as an answer though. You are correct that the company paying out \$1 in dividends drops the value of the company by \$1. You are also correct that it is more complicated than this. Here are some things to consider: The dividend yields of stocks also drive demand for ... 3 A long equity forward position initiated at$t=0$for delivery at$T$can be replicated by borrowing cash to purchase the stock at$t=0$, carrying that stock up to$T$and paying the interests on the cash borrowed (cash & carry). This shows that the forward price is basically the cost of funding the equity purchase. Now if the stock pays dividends the ... 3 Well, consider using$S_t$as the numeraire and let the asset be the reinvested stock$S_te^{qt}$. Then this ratio equals$e^{qt}$so can never be a martingale. 3 There is no real "risk-free" rate. Now to answer your question,$r$is time-dependent and should correspond to the repo rate corresponding to the maturity of your forward. In$I$, dividends should be "discounted" using the same time-dependent repo rate. Contrary to what others have suggested here, the use of an OIS rate or some other rate is not ... 2 In real life, you imply the unknown dividend yields from the forwards and the discount curve. 2 As a first Idea I would propose to incorporate basic ideas of Behavioural Finance and Dividend Theory into your considerations; for reference, look at: Baker, Malcolm, and Jeffrey Wurgler. Behavioral corporate finance: An updated survey. No. w17333. National Bureau of Economic Research, 2011. They state that investors prefer rather smooth dividend ... 2 Some recent US-listed stocks that have had stock dividends include: NYSE:TR ex-date 20160304 (3% stock dividend, plus also a cash dividend this day too) NYSE:EEQ ex-date 20160203 (3.582842% stock dividend) NASDAQ:SNFCA ex-date 20160113 (5% stock dividend). A stock dividend is effectively a tiny stock split. In the case of a 5% stock dividend, it's the ... 2 Assume that the time$t$forward for the maturity$T > t$is given by $$F_t(T) = \left( S_t - D_t(T) \right) e^{r (T - t)},$$ where$D_t(T)$is the time$t$value of all dividends paid over$(t, T]$. Consider a European contingent claim with time$t$value$V_t$. Then \frac{\partial V_t}{\partial S_t} = \... 2 If you are not able to find a data set, containing the dividend yield information for all the companies listed in ASX20/50/100/200/300, the only way is for you to make it by researching the companies. However I found this dividend yield scan to get you started. Once you have the dividend yield rate for all the stocks in the given index, it is just a matter ... 2 Call-put parity writes (to see this, notice that$(S_T-K)^+ - (K-S_T)^+ = S_T - K $and take the discounted risk-neutral expectation$E^{\mathbb {Q}} [. \vert \mathcal {F}_0 ]$on both sides): $$C(K,T) - P(K,T) = DF ( F(0,T) - K )$$ with$DF = e^{-rT} $the discount factor, and$F(0,T)$the fair forward price given by $$F(0,T) = (S_0 - D^*)e^{rT}$$ ... 2 I believe the exact answer to the question of what the S&P 500 price number assumes you do with the dividends is that you do NOT receive them at all. They are not included in the calculation AFAIK. So, yes, the price of one of the 500 companies drops a bit with a dividend payment (actually on the ex-dividend date), and the index drops a tiny bit because ... 2 S&P indices usually use an adjusted float weighted methodology, in which a change in the index level is defined -- in the base case -- by a Laspeyres index:$\frac{I + \Delta I}{I} = \frac{\sum_i P_{i,1}*Q_{i,0}}{\sum P_{i,0}*Q_{i,0}} \,; \forall i \in I$where:$I$is the index level;$P_i$is the price of asset$i$; and,$Q_i$is the float adjusted ... 2 Remember that Black-Scholes formula applies to lognormally distributed (under$\Bbb{Q}$) terminal asset prices$S_T\$. It is convenient to write this assumption $$S_T \underset{\Bbb{Q}}{\sim} \ln \mathcal{N}\left( \ln(F(0,T))-\frac{1}{2}\sigma^2 T, \sigma^2 T \right) \tag{A}$$ since it shows that the forward price is the risk-neutral expectation of the ...

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To add to the above on a more practical note: In general, SP desks make money on the individual product when the underlying declines. Dividends make the underlying decline, hence they are naturally long dividends. Take an auto-callable product which is exercised if the spot is above a pre-determined strike each year and say the SP desk sells this ...

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You cannot say "the continuous dividend yield is providing the most accurate answer" because you haven't really defined the problem. Accurate in what sense? What we are doing here is modelling a real-world situation. In a real world situation for equity options, dividends are always discrete. So a numerical solution that handles dividends properly (say ...

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You do root search for such an equation. It works perfectly well assuming a solution exists given your parameters. Aside from this it is not clear to me why you would want to imply the interest rate from this. Are you trying to imply the effective rate of financing from futures investors ? For a useful reference on the forward price formula you can ...

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