CFA CFA Level 2 Option arbitrage question…help pls!

Option arbitrage question…help pls!

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    • Alta12
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      I understand that when a call option is overpriced in the market, then you sell the call and buy n shares using the hedge ratio.

      But why is it when a put option is overpriced in the market, you sell the put and SELL n shares?

    • lulu123
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      where did you see this? are you sure it’s sell shares?

    • Alta12
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      It’s in the Elan practice questions.

      ‘Since the put options is selling for more than its actual worth ($4 vs $3.05) we would sell the put and SELL n units of the underlying stock for each option sold.

      It doesn’t make sense to me.

    • Alta12
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      It’s based on a hedge portfolio.

    • Sophie Macon
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      The statement is correct @Alta12, @lulu123. Doing that will neutralise your position to the market, i.e. your position is not affected by changes in the market (delta = 0).

      To think of it visually:

      If you recall your put option ‘hockey stick’ charts, selling a put option gives you the following payoff

      You’re still exposed if stock price falls below put strike price (in the case of the chart, it’s 80). At this stage your delta is positive (as stock price increase, the value of your short put position increases). So how do you hedge that? By shorting the amount of shares equal to that delta, which ‘neutralises’ your market position and gives you a delta of 0.

    • vincentt
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      Hi @sophie, when stock price increases, how does the value of the short put increases?
      I thought the maximum value a short put would get up to the premium? The put buyer will never exercise a put option if the price is above the exercise so it will always cap at the premium (from a put seller’s perspective).

      I understand the concept of shorting a currency pair or option, but to short a share correct me if i’m wrong, is to borrow someone else’s share (for a certain amount of time) and sell it at the current price, then hoping that the stock price will fall, and then buy the same amount of shares at the current price (at time T) and return the same amount of shares back to the lender. Or is this just the usual plain selling of stocks that you are currently having in hand?

    • Alta12
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      Thanks Sophie.

      So in summary, to achieve delta = 0:

      1. Long call, short stock
      2. Long put, long stock
      3. Short call, long stock
      4. Short put, short stock

    • Sophie Macon
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      Yup @Alta12, summarised perfectly! The extent to the exact amount to short or long depends on the delta. I personally find that for derivatives, if you understand the concept by the hockey stick charts, it’s quite easy to see what you need to do to achieve 0 delta (payoff is flat and doesn’t fluctuate according to share price).

    • Sophie Macon
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      Hi @sophie, when stock price increases, how does the value of the short put increases?

      Yo @vincentt – it increases but as you rightly said below, it’s capped. Or in other words, the value increases if stock price is increasing up to strike price, after that the value is max at the option premium. Sorry I wasn’t clear!

      I thought the maximum value a short put would get up to the premium? The put buyer will never exercise a put option if the price is above the exercise so it will always cap at the premium (from a put seller’s perspective).

      Yes you’re right @vincentt. As you can see from the chart the relationship is only partly linear and I was referring to that (my bad, I should write clearly!).

      I understand the concept of shorting a currency pair or option, but to short a share correct me if i’m wrong, is to borrow someone else’s share (for a certain amount of time) and sell it at the current price, then hoping that the stock price will fall, and then buy the same amount of shares at the current price (at time T) and return the same amount of shares back to the lender. Or is this just the usual plain selling of stocks that you are currently having in hand?

      Both are possible and correct. It depends whether you own the stock in the first place or not. The first concept is prevalent in the crisis – and I have witnessed it myself – whereby pension funds lend out their shares for yield enhancement, and short sellers borrowed it to make a quick buck which prompted so much volatility in the stock market. Nowadays, the first method is more restricted/regulated activity to prevent speculation and market volatility.

      Hope this clarifies things!

    • vincentt
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      @sophie thx for the explanation so now the main question 🙂

      As I understand, delta tells you how much options you need to hedge off your exposure (stocks holding in this case). However, if part of the action were to sell off the stocks, then why do we even need to sell a put option as we are not even hedging anything?

      Unless, there’s some additional information in the question that I’m missing?

    • Sophie Macon
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      Oooh @vincentt don’t test me – I quite like derivatives 😉 And you know I love your questions!

      Delta’s meaning is slightly broader than that @vincentt. It shows you the sensitivity of your option’s value to a change in value of underlying asset. Some call it the hedge ratio, as you rightly pointed out.

      The case here mentioned by @alta12 is if someone spots a mispricing in the market and hence an arbitrage opportunity. Therefore, if you believe a put option is overpriced, you want to sell it, but you want to lock in a sure profit and not expose yourself to downside if the underlying asset’s price falls, hence you neutralise it by shorting stocks (of delta amount). Then all you hope is the put option price drops, which you can buy it back and make a profit on the mispricing of the option itself, rather than betting on performance of underlying asset.

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