16 votes
Accepted

Term structure of Equity returns

Intro: Duration-Based Asset Pricing Similar to bonds, we can define the duration of stock $i$ as $$ Dur_{i,t} = \sum_{s=1}^\infty s\cdot\frac{\mathbb{E}_t[CF_{i,t+s}]e^{-s r_{i,t}}}{P_{i,t}},$$ where $...
user avatar
  • 13.8k
14 votes

Difference between S&P 500 index and S&P 500 Total Return index?

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 ...
user avatar
  • 911
13 votes
Accepted

Cochrane on Return Predictability

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. ...
user avatar
  • 6,294
10 votes

Cochrane on Return Predictability

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 ...
user avatar
  • 1,856
8 votes
Accepted

Implied Dividend from American Options (in practice)

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 ...
user avatar
  • 14.4k
7 votes
Accepted

Implied vol and model calibration for an american option on a dividend paying stock - is there a market standard pricing model?

Theoretically, this is a more difficult problem than it looks like at first glance. Unfortunately, existing literature taking into account a proper dividend consideration is rare (at least from a ...
user avatar
  • 721
6 votes

The Dog That Did Not Bark?

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 ...
user avatar
  • 266
6 votes
Accepted

How to derive forward price on stock with continuous dividend

When the dividend yield $q$ is constant one can in fact derive a very simple forward formula under no model assumptions on $S_t$ (see (4) below). Only no arbitrage arguments are needed: The forward ...
user avatar
  • 1,419
5 votes

Difference between S&P 500 index and S&P 500 Total Return index?

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 ...
user avatar
  • 59
5 votes

Black Scholes and high dividend paying stocks

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 ...
user avatar
5 votes
Accepted

Put-Call Parity with dividends

Diviends or not, the put-call parity (with European options) always hold: $ C(S,K) - P(S,K) = F - K*DF $ In the RHS, dividends will impact the forward $F$ (higher dividends imply lower forward). So ...
user avatar
  • 604
5 votes

Term structure of Equity returns

The term structure of returns refers to returns on assets with the same underlying cash flows, where the return is measured over the same holding period, but for different maturities. The price of a ...
user avatar
  • 6,665
4 votes
Accepted

How does income tax affect the Ex-dividend behavior of a stock?

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 ...
user avatar
4 votes
Accepted

Structured product sellers and div swaps

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 ...
user avatar
  • 1,346
4 votes
Accepted

Total Returns From Adjusted Close Prices

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 ...
user avatar
4 votes
Accepted

Why can only non-dividend paying assets serve as numeraire?

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.
user avatar
  • 13.7k
4 votes
Accepted

A question about exercise from "Paul Wilmott introduces Quantitative Finance"

You ought to compare the $t$-values of two self-financing strategies, under the assumption that there exists a risk-free money market account and that the dividend is deterministic but proportional to ...
user avatar
  • 13.9k
3 votes

The Dog That Did Not Bark?

As it was pointed above the phrase is taken from Sherlock Holme's novel. It describes the case when the dog should have bark, but didn't. Now if we come to the Cochrane paper. He introduces the system ...
user avatar
3 votes

Dividend as a function of stock

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. ...
user avatar
  • 1,436
3 votes

Difference between S&P 500 index and S&P 500 Total Return index?

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....
user avatar
  • 31
3 votes

MonteCarlo simulation of stock prices using milstein scheme with dividend yield?

The right formula: $$ S_{t+\Delta t} = S_t+(r-q)S_t \Delta t+\sigma\,S_t \sqrt{\Delta t}\,Z+\frac{1}{2}\sigma^2\Delta t(Z^2-1)*S_t $$ We can extract the formula from the Brownian motion equation (...
user avatar
3 votes
Accepted

is there a dependence between an annotation date of stocks dividend payment and the end fiscal year

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,...
user avatar
  • 2,913
3 votes

How does income tax affect the Ex-dividend behavior of a stock?

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 ...
user avatar
  • 2,386
3 votes
Accepted

Role of next month's dividends in forward pricing

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 ...
user avatar
  • 13.9k
3 votes

Structured product sellers and div swaps

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 ...
user avatar
  • 151
3 votes

Free dividend data API for non-US stocks

Yahoo Finance For example BASF (listed in Germany): https://finance.yahoo.com/quote/BAS.DE/history?period1=796867200&period2=1589932800&interval=div%7Csplit&filter=div&frequency=1d ...
user avatar
  • 243
3 votes
Accepted

Equity Forward Price calculation

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 ...
user avatar
  • 1,163
3 votes

Is it possible to use options to increase the yield of a dividend paying stock?

The advantage is that you get to keep the option premium. The obvious drawback is that your option can be exercised. You’re effectively capping your maximum gains on stock price increase.
user avatar
  • 7,598
3 votes
Accepted

Do European call options increase in value when dividends are increased?

In your example, I believe it's assumed that the exercise date is after the dividend date. If the dividend date is after the exercise date, nothing happens. The value would decrease, consider the ...
user avatar
  • 7,598

Only top scored, non community-wiki answers of a minimum length are eligible