17
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 $...
- 15.2k
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 ...
- 951
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.
...
- 6,924
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 ...
- 1,886
9
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 ...
- 14.7k
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 ...
- 823
7
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 ...
- 2,003
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 ...
- 266
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 ...
- 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 ...
- 5,622
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 ...
- 624
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 ...
- 8,032
5
votes
Accepted
Why do we use the letter $q$ for dividends?
It seems it didn't take long before the case of continuous dividends was considered in the literature. Robert Merton's 1973 paper "Theory of Rational Option Pricing" considers the case of ...
- 8,438
4
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....
- 41
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 ...
- 5,622
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 ...
- 1,356
4
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 ...
- 161
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 ...
- 3,186
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.
- 16.6k
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 ...
- 14.5k
4
votes
Why do we need an ex-dividend date?
I think you are really concerned about the record date. The ex-dividend date itself is set by the exchange. See for example Nasdaq.
The firm issuing the stock manages the declaration date, record ...
- 8,143
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,...
- 2,888
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 ...
- 2,531
3
votes
Accepted
What is the analogue used by Hull to price European calls with known cash dividends?
Remember that Black-Scholes formula applies to lognormally distributed (under $\Bbb{Q}$) terminal asset prices $S_T$. It is convenient to write this assumption
$$ S_T \underset{\Bbb{Q}}{\sim} \ln \...
- 14.5k
3
votes
MonteCarlo simulation of stock prices using milstein scheme with dividend yield?
The right formula:
$$ 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 (...
- 31
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 ...
- 87
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 ...
- 14.5k
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
...
- 263
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 ...
- 1,370
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.
- 8,438
Only top scored, non community-wiki answers of a minimum length are eligible