Valuing a Principal-Protected Note with an Equity Participation Rate

# PPPN: participation rate, stocks and premium


# PPPN: participation rate, stocks and premium












I'm a student of financial engineering and am very new to all of this stuff. Now, I'm trying to make an "example of a beginners exercise", but alas, I don't have any clue on how to solve or even on how to begin this one. The exercise goes like this:

> Suppose you have a PPPN where the invester recieves at maturity date $80 \%$ of his investment plus a premium, defined by: \begin{equation} p \cdot N/S_0 \cdot (S_T - S_0)^{+}, \end{equation} where $(S_T - S_0)^{+} = \max(S_T - S_0,0)$ is the positive stock return over the period $[0,T]$ ($t=T$ is the time to the Maturity date), an investment $N$ and where $p$ is the participation rate. Now, set $p$ such that the product is attractive for investors and you have a certain margin.

In order for this exercise to get more real, I've chosen a stock at random, say Facebook, and assumed a maturity date of 13/12/2016. Here is the information of the stock found today, credits to yahoo finance:

I thought it would be wise to choose $N= S_0= 102.12$, so that the equation of the premium simplifies to:

\begin{equation} p \cdot (S_T-102.12)^{+}. \end{equation}

Unfortunately, that's where my insights end. I don't have any clue on how to make further progress on this problem. Personally, I would just set $p =100 \%$, so you get the maximum possible return, but that can't be right. Any ideas/pointers/solutions?

## Answer by Gordon (score 2)

https://quant.stackexchange.com/a/22306

In general, PPN is the short form for principal protected notes. Here, the principal, or notional, $N$ is generally return in full. I am a little confused why only 80 % is returned. It may be a contractual specification, and it is also called a PPN.

Regarding the variable interest, or premium in your term, is the return that the investor will achieve. In your specification, the variable interest is defined by \begin{align*} p N/S_0 (S_T-S_0)^+ &= pN \left(\frac{S_T}{S_0} -1 \right)^+. \end{align*} Note that $\left(\frac{S_T}{S_0} -1 \right)^+$ is the positive part of the return. Here, $p$ is usually called the participation rate, and $N$ is the notional.

In summary, this PPN will return 80 % of the notional $N$ to the investor, and will pay the investor a ratio of $p$ of the final equity return if it is positive. The value of this PPN is the sum of the value of a zero-coupon bond plus a ratio of a European option. The participation rate $p$ can be determined so that the PPN value is higher than the value for a direct deposit into a banking account.