Recovering Period Returns from a Cumulative Return Series
Summary
The document shows how to recover period returns from cumulative returns formed by compounding a series of asset returns. It starts from the relationship that cumulative wealth is the product of one plus each period’s return, minus one. To retrieve a missing period return, divide one plus the current cumulative return by one plus the previous period’s cumulative return, then subtract one.
The example uses a pandas DataFrame and also shows an expression involving both original returns and cumulative returns, followed by a suggestion to shift the result for alignment. The general recovery method requires the cumulative series to be correctly ordered and the prior cumulative observation to be available; the first period needs an initial value convention. The brief example does not discuss missing observations, multiple assets, or numerical edge cases such as a denominator of zero. Its core contribution is the inverse relationship between cumulative compounding and individual period returns.
Key ideas
- Cumulative returns are formed by compounding one plus each period’s return.
- A period return can be recovered by dividing current wealth by prior wealth and subtracting one.
- The first observation requires an initial cumulative value or another starting convention.
- DataFrame shifting can align recovered returns with the intended periods.
- The example does not address missing data or edge cases in the cumulative series.
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# Opposite of Tail-Risk Hedge (Established Vocabulary) # Opposite of Tail-Risk Hedge (Established Vocabulary) I'm working on a client memo explaining several approaches to equity hedging, and I'm looking for a not-too-technical term for a hedging strategy where I try to keep options near the money, as to have a quickly reacting hedge, expensive, but drastically reduced drawdown (hopefully). Of course, the opposite would simply be called tail-risk hedge, but what if I tighten the moneyness? I was thinking about core hedge, near-the-money hedge, continuously adjusted hedge, ... Obviously this is just a marketing buzzword, but is there some established word that will be understood by most? Also, clients are not too technical, so it may well be a fuzzy word, or not 100% accurate. ## Answer by levocap (score 1) https://quant.stackexchange.com/a/14129 If you are already long the stock, the way to hedge that risk is to go long a put and short a call, or what we call a option collar. This is also know as a "hedge wrapper" if you are trying to go for the marketing buzzword. Per Investopedia: The purchase of an out-of-the money put option is what protects the underlying shares from a large downward move and locks in the profit. The price paid to buy the puts is lowered by amount of premium that is collect by selling the out of the money call. The ultimate goal of this position is that the underlying stock continues to rise until the written strike is reached. ## Answer by scootscomputes (score 1) https://quant.stackexchange.com/a/14161 The "not too techincal" term is the protective put. It usually applies to buying 1 put per 100 shares of stock owned, but you can explain that you hedge less, if you don't put on the full protective put. The technical term is delta hedging. I have used this term with less sophisticated clients after I explained what it meant.
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