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Put expected rate of return. Therefore, if the risk premium of the underlying stock is positive, then, the expected return on a put is less than the expected return on the stock". And I would add that, in this case the expected return of the put is even lower than the risk free rate, since: In the formula this seems perfect.

However, what is the meaning of this? If the put expected return is less than the risk free rate, why should anyone want to invest in a put? Wouldn't they be better off just by investing in the risk free rate?

I was with the idea that the risk free rate was the minimum expected rate that any asset could have. I guess I am missing an important concept here but do not know which. If the risk premium on the underlying is positive, then the stock is expected to appreciate in value A put is a risk management vehicle meant to limit your downside risk and overall return variance.

You may expect a better return over a large number of simulations by simply investing in the risk free rate, however, you will see significant increase in the range of returns. You may see a lower expected return, but will also reduce your VAR as well. Going back to exam FM, think of a put as insurance on your house. You pay a significant premium over what your expected loss would be, but you can sleep easy at night.

Thank you very much for your reply. The first sentence is very clarifying. This means, that you should own the underlying asset to justify a rational purchase of a put. If you do not own the asset, and you do not have a specific view about the future behaviour of the underlying asset and want to speculate on ityou would never own a put in your portfolio, right?

And this is sort of off-topic but, how is this related with the CML and efficient frontier stuff? Will the market portfolio include a put? You would certainly consider shorting a stock or buying a put if you thought the stock was going to go down One of the fundamental assumptions in finance is that markets are efficient and that investors want to be compensated for the risks they take.

This leads to the assumption that markets will correct themselves until they offer the investor the required rate of return. This is obviously not how markets works since each individual investor has a different alpha as well as a different 1 year price outlook.

The efficient frontier is just an imaginary line that is the highest expected return for a given standard deviation risk. I THINK If you have a positive alpha, then a put has a negative expected return and can at best reduce your risk to 0, but expected rate of return on option generate a return less than the expected rate of return on option free rate which the point rf, 0 lies on the efficient frontier. This is not to say you can not generate a point on the efficient frontier by using puts and calls, that is a fact I'm not sure of, as the efficient frontier is generally considered to be a level of diversification.

The market portfolio is just another point on the efficient frontier used to expected rate of return on option it its the basket of all stocks and assumes that owning every stock gives you the lowest risk for the market return. These are nice theories but do not hold true in practice, it gives some structure to what is a chaotic market place.

You would buy a put when you thought an asset would depreciate in value and volatility will increase. If you have no volatility view you will simply short sell the asset. If you think volatility will decrease then you will sell calls.

If you think an asset will increase, and volatility will decrease then you would sell puts. From the stand point of managing an equity portfolio, a put would mostly be used to manage risk or reduce transaction costs.

Say you owned a portfolio of stocks and thought that market was going to crash. I hope this clears things up. Thank you very much for your thorough reply. If you think an asset will increase, and volatility will decrease then you would sell puts" 1 Why does the volatility defines whether to buy a put or short sell the asset? Is it because if I believe the volatility increases the put with the current price could be considered undervalued as valued with a expected rate of return on option volatility?

For me, the true probabilities will be different and expected rate of return on option put could be considered to be undervalued, right? I would be making an arbitrage, right? I mean, most of the formulas we study assume that arbitrage is not possible, right? If I have a different view, then I would believe arbitrage is available. What is the consequence of this apart from my belief that I could make tons of money with the arbitrage: Is there any implication, for example, in the calculation of the delta or if I want to hedge my position, or in the replicating portfolio?

Arbitrage is risk free profit If you short sell an asset and it depreciates you profit. If you buy a put and the the underlying depreciates there are 3 scenarios: Risk free profit is completely different then expected profit. It is possible to calculate a historic volatility, but what happens is people assume black scholes holds true and will insert all the known factors into the equation along with the market price and calculate the "implied volatility" simply the volatility suggested by the markets current price and then make there decisions based upon their opinions about what the true volatility should be Is the market volatility really incorrect?

Delta changes every second with every tick of the stock, with every second that elapses, with every change in volatility. This is why you pay an option premium, this goes towards paying for the expected loss of the market maker by delta hedging.

They then make their money by charging a expected rate of return on option spread and with contract fees. You are absolutely right about arbitrage. What I wrote is wrong unless I have the crystal ball to predict the future and my expectations are always correct: Suppose that I have a different view of the market volatility but no specific view about the asset behaviour and I want to buy expected rate of return on option option for example if I have an asset and I want to temporarily hedge it with an option.

Should I use my estimate of future volatility in calculating Delta N d1 and Gamma N' d1or should I use the market implied volatility. I believe I should use my particular expectation, right? It is as if I would build my particular binomial tree with a different volatility, isn't it so?

You can plug whatever volatility you want into the formula, but regardless you pay the market price with the implied expected rate of return on option. That's why you decide what to do short sell, buy put, sell call based on the implied vol vs your expectation of vol.

Delta will not be the same under different volatilities and, then the number of options or stock I need to buy to make the hedge will be different, isn't it? Delta hedging is for market makers and an inexact science designed to make you break even in aggregate. You need to constantly adjust your hedge to achieve a 0 delta position, your variance will shrink the more often you hedge. In practice, market makers may readjust their hedge every expected rate of return on option or 2. I wish this test was a required course instead of a test because it really doesnt provide any insight to the beauty of black scholes to present it simply as a formula.

Stochastic calculus is a beautiful thing, and the price presented by black scholes can be obtained by using geometric brownian motion to model a stocks movement, black scholes delta hedging, and monte carlo simulation to find the expected loss of the delta hedge.

You can try to use other methods of hedging other than black scholes delta-hedging, and they can give you a close expected loss, but the beauty in black scholes is that the variance of the expected loss decreases without bound as you increase the frequency of your hedge. OK, sorry to ask again but: To the expected rate of return on option volatility or to his one estimate of future volatility? But is it only for market makers of options. Can't you delta hedge a possition in the underlying by buying options?

Would it be reasonable to do so in any context? However, I believe that most candidates included myself of course have absolutely no possibility of learning stochastic calculus properly and understand it fully never in our lives wiener, itostratonovich, girsanov, caratheodory, lebesgue, bellman and zillions of other surnames with their own theories and theorems.

Therefore, we should conform ourselves with reading the Mcdonalds and only grasp the very basic concepts. The market maker uses the implied volatility because he expected rate of return on option to offset is delta position Remember, delta is the calls sensitivity to a price change in the underlying. So a market maker wants to have no risk associated with the stock price of course he still has risk of large price movements, thats where Gamma hedging comes in, but thats unusual The market maker is attempting to replicate the option with a stock position so he has no risk.

You could execute a expected rate of return on option delta hedge using options, although delta hedging is very similar to insurance in that it only makes sense in aggregate because you can still experience large losses. Delta hedging your portfolio one time would be similar to just insuring the expected rate of return on option property. The material is presented in McDonald to be much more difficult then it really is and that's not thier fault its just more of a expected rate of return on option on topic.

I'm in the same boat as you preparing for the exam right now and I'm kind of worried about whether I'll pass it which is ironic because I can and have applied most of the topics in practice.

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Stock option return calculations provide investors an easy metric for comparing stock option positions. For example, for two stock option positions which appear identical, the potential stock option return may be useful for determining which position has the highest relative potential return.

A covered call position is a neutral-to-bullish investment strategy and consists of purchasing a stock and selling a call option against the stock. The Bull Put Credit Spread see bull spread is a bullish strategy and consists of selling a put option and purchasing a put option for the same stock or index at differing strike prices for the same expiration. The purchased put option is entered at a strike price lower than the strike price of the sold put option.

The return calculation for the Bull-Put Credit Spread position assuming price of the stock or index at expiration is greater than the sold put is shown below:. The Bear Call Credit Spread see bear spread is a bearish strategy and consists of selling a call option and purchasing a call option for the same stock or index at differing strike prices for the same expiration.

The purchased call option is entered at a strike price higher than the strike price of the sold call option. The return calculation for the Bear Call Credit Spread position assuming price of the stock or index at expiration is less than the sold call is shown below:.

The iron condor is a neutral strategy and consists of a combination of a bull put credit spread and a bear call credit spread see above.

Ideally, the margin for the Iron Condor is the maximum of the bull put and bear call spreads, but some brokers require a cumulative margin for the bull put and the bear call. The return calculation for the Iron Condor position using the maximum margin of the bull put credit spread and the bear call credit spread and assuming price of the stock or index at expiration is greater than the sold put option and less than the sold call option is shown below:.

The return generated for this position is:. The collar finance is a neutral-to-bullish strategy and consists of a combination of a covered call see above and a long put option for protection. The protective put provides insurance to guarantee a floor on the potential loss, but the protective put option also reduces the amount of potential return.

The collar is useful for reducing or delaying taxes for large stock positions which otherwise would need to be sold in order to diversify, reduce risk, etc. The following calculation assumes the sold call option and the purchased put option are both out-of-the-money and the price of the stock at expiration is the same as at entry:. The break-even point is the stock purchase price minus the net of the call option price and the put option price.

The percent maximum loss is the difference between the break-even price and the strike price of the purchased put option divided by the net investment, for example for JKH:. The naked put is a neutral-to-bullish strategy and consists of selling a put option against a stock. The naked put generally requires less in brokerage fees and commissions than the covered call. The following return calculation assumes the sold put option is out-of-the-money and the price of the stock at expiration is greater than the put strike price at option expiration:.

The calendar call spread see calendar spread is a bullish strategy and consists of selling a put option with a shorter expiration against a purchased call option with an expiration further out in time.

The calendar call spread is basically a leveraged version of the covered call see above , but purchasing long call options instead of purchasing stock. The long straddle see straddle is a bullish and a bearish strategy and consists of purchasing a put option and a call option with the same strike prices and expiration.

The long straddle is profitable if the underlying stock or index makes a movement upward or downward offsetting the initial combined purchase price of the options. A long straddle becomes profitable if the stock or index moves more than the combined purchase prices of the options away from the strike price of the options.

The iron butterfly is a neutral strategy and consists of a combination of a bull put credit spread and a bear call credit spread see above. The iron butterfly is a special case of an iron condor see above where the strike price for the bull put credit spread and the bear call credit spread are the same. Ideally, the margin for the iron butterfly is the maximum of the bull put and bear call spreads, but some brokers require a cumulative margin for the bull put and the bear call.

The maximum return generated for the iron butterfly is when the stock price is the same as when the position was entered. The return calculation for the iron butterfly position using the maximum margin of the bull put credit spread and the bear call credit spread and assuming price of the stock or index at expiration is the same as when the position was entered is shown below:.

Iron Butterflies have higher returns than iron condors, but the stock price range where the iron butterfly position is profitable is much less than for the iron condor. The married put also known as a protective put is a bullish strategy and consists of the purchase of a long stock and a long put option. The married put has limited downside risk provided by the purchased put option and a potential return which is infinite.

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