Apoorva Javadekar - My comments on pricing and timing of dividend

On the Timing and Pricing of Dividends
Binsbergen, Brandt, Koijen
Presented by Apoorva Javadekar
Boston University, Class of EC 745
March 4, 2012
Presented by Apoorva Javadekar (Boston University, Class of EC 745)Pricing Dividends March 4, 2012 1 / 17

Introduction
Lucas(1978): Total wealth is the price of a claim to all future
consumption
Gordon(1962): Value of aggregate stock market equals sum of
discounted future dividends
Central Question: How to discount future cash ﬂows to value an
asset today
Main Ingredients: Future Cash Flows and Discounting rates
These two ingredients might behave diﬀerently in short term versus
long term. Hence, it might be interesting to decompose the asset
prices in to short term component and long term component.

Paper Broadly
What does Paper do?
asset price = price of short term beneﬁts + price of long term
beneﬁts
Creates short term asset called ”dividend strips”: Paying dividends only
(No price risk)
Prices the asset using ’no arbitrage’ condition.
Studies Time series properties of prices
Why to study Short term prices
Recover discount rates implicit in asset prices as a function of maturity
Understand investor’s risk preferences as a function of maturity of the
asset
Study other time series properties of the short term and long term
components of the value of the asset
Derive some implications for other models

Model Broadly II: Conclusions
E(R), σ(R), Sharpe ratios are higher for short term leg of the asset
than corresponding statistics for asset itself
Beta of the short term assets (against market index) is around 0.5
CAPM α is around 10%. and does not vary much even when other
factors are added in regression
Short term asset returns are predictable.
Excess Volatility features for short term asset as well; Price vary
more than subsequent short term dividend realizations.

Basic Mechanism
Value of Equity: Let {Dt+i }∞
i=1 be the dividend process. Then
St =
∞
i=1
Et(Mt:t+i Dt+i ) (1)
where Mt:t+i = i
j=1 Mt+j
This just says that asset price is sum of discounted value of dividends.
Decomposition
St =
T
i=1
Et(Mt:t+i Dt+i ) +
∞
i=T+1
Asset Value = Short term value + Long term value
Objective Find out the price of the short term beneﬁts. Call it Vt,T
Vt,T =
T
i=1

Pricing Strategy: Theory
Using Put - Call Parity (Augmented for Dividends)
ct,T + Xe−rt,T (T−t)
= pt,T + St − Vt,T (4)
This holds because St is cum - dividends and trading in options do
not give access to dividends. So for ’no arbitrage’ condition, we
need to consider ex-dividend price of stock.
Using Futures Contract: Let Ft,T be the futures price determined
at t for which one unit of stock will be delivered after T periods
Ft,T e−rt,T (T−t)
= St − Vt,T (5)
This holds because one can get ex - dividend stock at T by buying
futures today for which required cash is given by L.H.S
Both these relationships assume only ’No Arbitrage’ to hold.

Pricing Implementation: Data
Underlying Index: S&P 500.
Data Period: Jan 1996 - May 2009
Options Data: CBOE intra day Quotes and Trades on S&P 500 of
all options for which S&P 500 is an underlying
Index Values and Futures Values: From Tick Data Inc - Minute
level data available for index values and futures prices
Interest Rates: Collection of ZCB rates for various maturities. Zero
curve derived using LIBOR and EURODOLLAR futures
Dividends: S&P 500 returns data with and without distribution from
S&P Index services
Cash Div = (Diﬀerential returns) × lagged index value (6)

Pricing Implementation: Data Matching
Minute Level Matching: All the data matched on last trading day
of each month within a particular minute.
As options market closes 15 Minutes after the stock market, matching
ending quotes is biased.
Options data used as LEAPS data for longer maturities available
For a given Maturity;
1 ﬁx some strike price
2 Get quotes on all call options matching these two parameters
3 For each call quote, ﬁnd ’closest in time’ put quote with same
parameters
4 Keep a pair which has quotes ’closest in time’
5 Compute dividend price for given maturity for each such match
6 Repeat it for each available strike price.
V(for given maturity) = Median of all such prices

Dividend Steepner
Both the options and futures strategies require exposure to stock
index. Replicating stock index is costly
To avoid this problem, we can study price of dividends paid between
two futures dates: t < T1 < T2
Dividend Steepner exposes investor to only dividends between T1 and
T2 without replicating index.
Value of Steepner
Vt,T1,T2 = Vt,T2 − Vt,T1 (7)

Empirical Findings: Dividend Prices
Prices increase monotonically with maturities (does not violate
’No arbitrage’)
Prices drop during recessions: Expected growth of dividends drop
during recession and discount rate rises
Stationarity: Divide prices by Index values
1 Ratios for various maturities are strongly correlated
2 Ratio dropped in 2001 recession, increased in 2009 recession
3 Suggestive of the fact that current recession is long lasting (recession
aﬀects index values more than div. prices)

Empirical Findings: Dividend Returns
Deﬁning returns
Rt+1 =
V(t+1,T−1) + Dt+1
Vt,T
(8)
High returns: 14.40% annualised as against S&P 500 return of 5.9%
annulized
Higher volatility: Returns volatility = 7.9%, S&P 500 return
volatiltiy = 4.7%
Still results in higher Sharpe Ratios: almost twice
This corresponds to Duﬃe (2010): Lower SR for longer term
Treasuries
Beta of around 0.5 with market returns and CAPM α = 10%
Regression intercept does not change much even with additional
factors; (book to market etc). ⇒ Short term asset returns are not
explained by standard asset pricing models.

Empirical Findings: Dividend Returns Predictability
Dividend returns are mean reverting
Rt+1 = β0 + β1
V(t,T)
Dt
: Statistically signiﬁcant with -ve sign (Table 6)
Expected returns and expected dividend growth are predictable
Expected returns are more persistent
Puzzle: High predictability and high volatility

Empirical Findings: Excess Volatility
Shiller: Prices more volatile than subsequent dividends ⇒ excess
volatility
Why? Discount ﬂuctuate over time and long duration of stocks ⇒
high volatility in prices
But same characteristics observed for Short term prices (Figure 9)
Hence, explanation of excess volatility must explain both long term
and short term excess volatilities.

Prices in equilibrium Model: Lucas Economy
Basic model
∆(ln(ct+1)) = g + t+1, t+1 ∼ N(0, σ2
) (9)
k- period SDF
Mt:t+k = βk Ct+k
Ct
−γ
(10)
Price
Vt,t+k =
k
s=1
exp s ln β + s(1 − γ)g +
s
2
(1 − γ)2
σ2
(11)

Prices in equilibrium Model: Comparison
Model prices computed using same calibration as in the original papers
Prices and properties do not match with ’No Arbitrage’ prices
Reason: Shock structure in these models not speciﬁc to match short
term dividend prices
Habit Model (1999) and LLR Model (2004): Risk premium near
zero, σ(R), SR are lower
Rare Disaster Model: E(R) constant over maturities, volatility lower
for short term as compared to long term
Lettau and Watcher (2007): Matches with this model. Beta is also
well below 1

Robustness
Results hold more or less for alternative matching criterion:
moneyness, bid-ask spread etc
Results hold for futures contract strategy too

Comments on the paper
What I liked:
Robust, Market based story: Uses only ’No Arbitrage Condition’
Pricing in terms of liquid assets: Liquidity risk does not enter the
dividend prices
Potentially marketable security: (dividend steepner)
Contribution: Insight on excess volatility puzzle: need for joint
explanation
Few concerns:
Does out of money options aﬀect the pricing?
Possibility of pricing individual dividend strips? discrete dividends
As dividend swaps are available: Do the ’No arbitrage prices matches
with market prices’?
Fail to understand what attracted the attention to the paper?

Apoorva Javadekar - My comments on pricing and timing of dividend

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