The Goal

The goal of Portfolio Insurance is to replicate a protective put position without using a put option.

Why?

A put option on your portfolio may not exist because:

• Your portfolio is unlike any index.
• The maturity of traded put options may not match the period for which you want protection.

Local Protective Put Replication

The approach taken by portfolio insurance is simply to replicate the protective put over a small set of underlying portfolio values. That is we replicate the protective put locally.

• But since our approach will only work locally, we'll have to constantly rebalance it for it to work globally, i.e. over every value of the underlying portfolio.

An Example

Say we have a portfolio worth \$100, and we want to ensure we don't lose more than \$20 over the next year.

• We want a put option on the portfolio with an \$80 exercise price.
• Assuming no such put option exists, we'll employ portfolio insurance.

Locally What Does a Protective Put Mean

While we can't buy the put we want, we can still calculate the Greeks for the put option.

• Using the Delta app at the above link, we can see the Delta is -0.09 (assuming 20% volatility, and a 2% risk-free rate).
• This means if our portfolio falls by \$1, then the put would increase by \$0.09, and the total change in a protective put position would be -\$0.91.

Recreating the Protective Put

What if we simply sold 9% of our portfolio and held it in cash?

• Then we would hold \$91 of the portfolio, and if it went down by \$1 we would lose -$0.91.
• So, locally, the protective put is equivalent to selling 9% of our portfolio.

Rebalancing

This only works locally because as the portfolio value changes, the put's Delta also changes.

• If the portfolio's value is \$99, then the put's Delta is -0.10.
• So to recreate the protective put we now have to sell \$1 of our portfolio, so we have \$90 in the portfolio and \$10 in cash.

Rebalancing Again

How Often Should You Rebalance?

Look at the options Gamma (which is the rate of change in the Delta). The greater the gamma, the more often you have to rebalance. Note, gamma tends to be greatest at the money.

• See this presentation for an interactive app to calculate gamma.

Portfolio Insurance (Put Strike) at $50

Portfolio Value:

Put Delta =

Put Gamma =

Momentum

Employing portfolio insurance

Taxes

To implement portfolio insurance on your portfolio, you must buy/sell the portfolio.

• Selling part of your portfolio may realize a taxable capital gain.
• Thus portfolio insurance may be more appropriate in a tax-shielded account.

Credits and Collaboration

Click the following links to see the code, authors of this presentation.

If you would like to make any additions or corrections to this presentation, visit our GitHub repository page to learn more about how to contribute.