Tracking Stock Values Through Fixed Discrete Dividends

Summary

The document asks how to value a stock across a two-period binomial tree when it pays fixed cash dividends. It starts with a stock price of 100, up and down factors of 1.2 and its reciprocal, and dividends of 10 and 5 in successive periods. The author calculates ex-dividend stock values by applying each period’s price move and subtracting that period’s dividend, then lists the resulting four paths at time two.

This is a worked setup for understanding how dividends affect tree values, but it does not provide an answer or verify the calculations. The interpretation depends on what the tree’s up and down factors represent and whether the underlying values are specified before or after dividend payment. A portfolio that includes reinvested dividends or cash distributions would have different total values from the ex-dividend stock alone; the document leaves that distinction unresolved.

Key ideas

• A fixed cash dividend reduces the stock’s ex-dividend value when it is paid.
• The example applies each period’s up or down factor before subtracting that period’s dividend.
• A two-period tree produces four possible price paths by the second period.
• The listed calculations require clarification about whether the tree values represent ex-dividend prices or total portfolio wealth.

Tags

# Value of portfolio with fixed discrete dividends


# Value of portfolio with fixed discrete dividends












I know that this is a very simple question, but i want to make sure to grasp the concept of ex dividend and value of portfolio.

Suppose that we have a two period binomial tree of a stock with initial value of $S_0= 100$ and $u=1.2$ and $d=1/u$. The stock pays fixed discrete dividends: $d_1=10$ in the first period and $d_2= 5$ in the next period.

What is the Value of this portfolio at times $1$ and $2$?

$1)$ If the stock goes up then: $V_1= 100*(1.2)-10=110$

if the stock goes down then $V_1=100*(1/1.2)-10=73.33$

$2)$ if the stock goes up up then: $V_2= 110*(1.2)-5=115$

if the stock goes up and down then $V_2= 110(1/1.2)-5=86.66$

if the stock goes down and up then $V_2= 73.33(1.2)-5= 83$

if the stock goes down and down then $V_2= 73.33(1/1.2)-5= 56.11$

I would really appreciate if you can tell me if this is the correct value of the portfolio, or if I´m doing something wrong.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.