Synthetic Equity
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Synthetic
Equity
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Here I provide a way to understand synthetic equity.
Suppose you are holding treasury bill = T0. How can
you construct such that you are equivalently holding equity?
Of course, you can sell the T bills and buy the
equity. But in many cases you don’t (or cannot) do so. What you can do is to
buy futures of that equity. Let’s say the equity is an index. At time t, you
will have
T_t = T0 * (1+rf)^t
You can use this money to fulfill the future
contracts. So, it means today you can buy the following number of contracts:
T_t / (index * multiplier)
So, just go ahead to buy this amount of contract and
you will
1) be able to
fulfill the contract because you do have money from T-bill at expiration
(t)
2) gain or lose just like holding the equity
Sometimes, you may need to purchase additional T-bill
today inorder to make a rounded number of futures contract.
You can see we have changed the nature of the holdings
without physically changed it.
Completely wrong appoach; Let’s start from the very beginning: you wish turn beta from zero. Classical formula works only and if: futures’ beta is equal to equity’s beta; Futures’ beta for the same stock is always less, present value factor is, as usually, 1/(1+r)*T. (very sophisticated math.)
You can never create equity desired with futures’ beta different from the stock’s desired one… See curriculum…
Sample 2007, 2008 CFA exams’ answers to the issue are incorrect.
Not sure if I understand you correctly. But this is to create Synthetic Cash not to adjust beta. Please point out the page numbers of the curriculum you are referring to or the sample exams numbers. Thanks!
1. this is to create synthetic equity, not cash. 2. to create synthetic equity means to turn beta from zero (see previous comment). 3. My pleasure. 2009 Level 3 CFA Curriculum, V.5. P.333 (just after Example 5)