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<!doctype html>
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<title>Study Session 15 | Reading 37 | Risk Management Applications of Option Strategies</title>
<meta name="description" content="Chartered Financial Analyst Level 3 Study Materials">
<meta name="author" content="MacLane Wilkison">
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<section>
<h1>Reading 37</h1>
<h3>Risk Management Applications of Option Strategies</h3>
<p>
<small>Created for <a href="http://alchemistsacademy.com">Alchemists Academy</a> by <a href="http://alchemistsacademy.com/about">MacLaneWilkison</a></small>
</p>
</section>
<section>
<h2>Covered Call</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=S<sub>T</sub>-max(0,S<sub>T</sub>-X)</li>
<li>Profit: Π=V<sub>T</sub>-S<sub>0</sub>+c<sub>0</sub></li>
<li>Maximum profit: X-S<sub>0</sub>+c<sub>0</sub></li>
<li>Maximum loss: S<sub>0</sub>-c<sub>0</sub></li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=S<sub>0</sub>-c<sub>0</sub></li>
</ul>
<aside class="notes">
A covered call is a relatively conservative strategy in which you own the underlying and sell a call.
</aside>
</section>
<section>
<h2>Protective Put</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=S<sub>T</sub>+max(0,X-S<sub>T</sub>)</li>
<li>Profit: Π=V<sub>T</sub>-S<sub>0</sub>-p<sub>0</sub></li>
<li>Maximum profit: ∞</li>
<li>Maximum loss: S<sub>0</sub>+p<sub>0</sub>-X</li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=S<sub>0</sub>+p<sub>0</sub></li>
</ul>
<aside class="notes">
A protective put entails holding an asset and a put on the asset to protect against downside risk.
</aside>
</section>
<section>
<h2>Bull Spread</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=max(0,S<sub>T</sub>-X<sub>1</sub>)-max(0,S<sub>T</sub>-X<sub>2</sub>)</li>
<li>Profit: Π=max(0,S<sub>T</sub>-X<sub>1</sub>)-max(0,S<sub>T</sub>-X<sub>2</sub>-(c<sub>1</sub>-c<sub>2</sub>)</li>
<li>Maximum profit: X<sub>2</sub>-X<sub>1</sub>-c<sub>1</sub>+c<sub>2</sub></li>
<li>Maximum loss: c<sub>1</sub>-c<sub>2</sub></li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=X<sub>1</sub>+c<sub>1</sub>-c<sub>2</sub></li>
</ul>
<aside class="notes">
A bull spread combines a long position in a call with one exercise price and a short position in a call with a higher exercise price. As its name implies it's designed to make money when the market goes up.
</aside>
</section>
<section>
<h2>Bear Spread</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=max(0,X<sub>2</sub>-S<sub>T</sub>)-max(0,X<sub>1</sub>-S<sub>T</sub>)</li>
<li>Profit: Π=V<sub>T</sub>-p<sub>2</sub>+p<sub>1</sub></li>
<li>Maximum profit: X<sub>2</sub>-X<sub>1</sub>-p<sub>2</sub>+p<sub>1</sub></li>
<li>Maximum loss: p<sub>2</sub>-p<sub>1</sub></li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=X<sub>2</sub>-p<sub>2</sub>+p<sub>1</sub></li>
</ul>
<aside class="notes">
A bear spread can entail selling a call with a lower exercise price and buying a call with a higher exercise price OR buying a put with a higher exercise price and selling a put with a lower exercise price.
</aside>
</section>
<section>
<h2>Butterfly Spread</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=max(0,S<sub>T</sub>-X<sub>1</sub>)-2max(0,S<sub>T</sub>-X<sub>2</sub>)+max(0,S<sub>T</sub>-X<sub>3</sub>)</li>
<li>Profit: Π=V<sub>T</sub>-c<sub>1</sub>+2c<sub>2</sub>-c<sub>3</sub></li>
<li>Maximum profit: X<sub>2</sub>-X<sub>1</sub>-c<sub>1</sub>+2c<sub>2</sub>-c<sub>3</sub></li>
<li>Maximum loss: c<sub>1</sub>-2c<sub>2</sub>+c<sub>3</sub></li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=X<sub>1</sub>+c<sub>1</sub>-2c<sub>2</sub>+c<sub>3</sub> AND S<sup>*</sup><sub>T</sub>=2X<sub>2</sub>-X<sub>1</sub>-c<sub>1</sub>+2c<sub>2</sub>-c<sub>3</sub></li>
</ul>
<aside class="notes">
A butterfly spread combines a bull and a bear spread. It is a bet that the volatility of the underlying will be relatively muted.
</aside>
</section>
<section>
<h2>Collars</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=S<sub>T</sub>+max(0,X<sub>1</sub>-S<sub>T</sub>)-max(0,S<sub>T</sub>-X<sub>2</sub>)</li>
<li>Profit: Π=V<sub>T</sub>-S<sub>0</sub></li>
<li>Maximum profit: X<sub>2</sub>-S<sub>0</sub></li>
<li>Maximum loss: S<sub>0</sub>-X<sub>1</sub></li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=S<sub>0</sub></li>
</ul>
<aside class="notes">
A collar is the strategy of offsetting a call premium with a put premium or vice-versa (the prices are determined using the Black-Scholes-Merton option pricing formula). Cases in which the premiums exactly offset are referred to as zero-cost collars.
</aside>
</section>
<section>
<h2>Straddle</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=max(0,S<sub>T</sub>-X)+max(0,X-S<sub>T</sub>)</li>
<li>Profit: Π=V<sub>T</sub>-(c<sub>0</sub>+p<sub>0</sub>)</li>
<li>Maximum profit: ∞</li>
<li>Maximum loss: c<sub>0</sub>+p<sub>0</sub></li>
<li>Breakeven: S<sup>*</sup><sub>T</sub>=X±(c<sub>0</sub>+p<sub>0</sub>)</li
</ul>
<aside class="notes">
A straddle is the purchase of both a call and a put with the same exercise price on the same underlying with the same expiration. It is a bet on volatility. If the investor believes an upward move to be more likely she may purchase an additional call, creating a strap. If the investor believes a downward move to be more likely she may purchase an additional put, creating a strip. Finally, a strangle is the purchase of a put and call with different exercise prices.
</aside>
</section>
<section>
<h2>Box Spread</h2>
<ul>
<li>Value at expiration: V<sub>T</sub>=X<sub>2</sub>-X<sub>1</sub></li>
<li>Profit: Π=X<sub>2</sub>-X<sub>1</sub>-(c<sub>1</sub>-c<sub>2</sub>+p<sub>2</sub>-p<sub>1</sub>)</li>
<li>Maximum profit: Π</li>
<li>Maximum loss: no loss possible</li>
<li>Breakeven: n/a</li>
</ul>
<aside class="notes">
A box spread is the combination of a bull and bear spread. Assuming fair option prices, the investor always receives the risk-free rate.
</aside>
</section>
<section>
<h2>Interest Rate Call</h2>
<ul>
<li>Notional principal × max(0, Underlying rate at expiration - Exercise rate) × (Days in underlying rate / 360)</li>
<li>Interest rate caps</li>
</ul>
<aside class="notes">
A cap is a combination of interest rate call options structured to "cap" the interest rate on a loan. The individual constituent options are referred to as caplets.
</aside>
</section>
<section>
<h2>Interest Rate Put</h2>
<ul>
<li>Notional principal × max(0, Exercise rate - Underlying rate at expiration) × (Days in underlying rate / 360)</li>
<li>Interest rate floors</li>
</ul>
<aside class="notes">
A floor is a combination of interest rate put options structured to provide a "floor" on the interest rate on a loan. The individual constituent options are referred to as floorlets.
</aside>
</section>
<section>
<h2>Interest Rate Collar</h2>
<ul>
<li>Long position in cap combined with short position in floor</li>
<li>Proceeds from sale of the floor offset cost of the call</li>
<li>Establishes a range in which the effective interest rate on the loan can vary</li>
</ul>
</section>
<section>
<h2>Option Portfolio Risk Management</h2>
<ul>
<li>Delta hedging</li>
<ul>
<li>Delta ≈ Change in option price / Change in underlying price</li>
<li>N<sub>c</sub>/N<sub>s</sub>=-1/(Δc/ΔS)</li>
<li>Estimated option price = Original option price + (New underlying price - Original underlying price) × Delta</li>
</ul>
</ul>
<aside class="notes">
Delta is merely an approximation of the change in the call price for a change in the underlying. Delta changes if anything else changes(i.e. the price of the underlying or time). The number of units of the underlying must be rounded off, leading to a small amount of imprecision in the delta hedge. Be careful, delta is not an accurate estimation for large changes in price. 'N<sub>s</sub>' is the number of units of the underlying. 'N<sub>c</sub>' is the number of call options. The ratio of calls to shares equals -1/delta. We use the Black-Scholes-Merton model to determine the price of the option.
</aside>
</section>
<section>
<h2>Other Measures</h2>
<ul>
<li>Gamma = Change in the delta / Change in the underlying price</li>
<li>Vega = Change in option price / Change in volatility</li>
</ul>
<aside class="notes">
Rapid changes in delta are more likely to occur in options that are at-the-money and/or near expiration. It is under these conditions that gamma is largest. Vega is the sensitivity of the option price to volatility.
</aside>
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
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