40 lines
3.2 KiB
Plaintext
40 lines
3.2 KiB
Plaintext
Chapter 28: Mathematical Applications 481
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action point (recall that the collateral requirement increases for naked options on an
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adverse stock movement), and the break-even points themselves. The probabilities of
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being above the upper break-even point at expiration or below the lower break-even
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point should be computed as well. Moreover, an expected return analysis could be
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performed on the position to determine the general level of profitability of the posi
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tion with respect to all other positions of the same type on other stocks. Such an
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expected return analysis need not assume that the position is held to expiration. Firm
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traders, paying little or no commissions, might be interested in seeing the expected
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reswts for a holding period as short as 30 days or less. Public customers might use a
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longer holding period, on the assumption that they would not trade the position as
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readily because of commission costs. Ratio positions should be ranked either by
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return if unchanged or by expected return.
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The analyses described for calendar spreads and ratio positions should not be
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relied upon as gospel. In the proposed forms of analysis, one is projecting future
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option prices and stock prices under the assumption that the volatility of the under
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lying stock will remain the same. Although this may be true in some cases, there will
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also be many times when the volatility of the underlying stock will change during the
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life of the position. If the volatility decreases, the projected break-even points for a
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calendar spread will be too far away from the striking price. Thus, a loss would result
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at some prices where the spreader expected to make money. If the volatility increas
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es, the expected return of a ratio position will drop, because the probabilities of the
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stock moving outside the profit range will increase, thereby increasing the probabil
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ity ofloss.
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The effect of a changing volatility can be counteracted, in theory, by continuing
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to monitor the position daily after it has been established. In a straddle write, for
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example, if the stock begins to move dramatically, the expected return may become
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very low. If this happens, adjustments could be made to the position to improve it.
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Such monitoring is difficult to apply in practice for the public customer, because the
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commission costs involved in constant position adjustments would mount rapidly.
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There is no exact method that would allow for infrequent, periodic adjustments, but
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by using a follow-up analysis the public customer may be able to get a better feeling
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for the timing of adjusting a position. For example, suppose that one initially wrote a
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5-point straddle when the stock was at 30. Sometime later, the stock is at 34. The
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expected return of writing a 5-point straddle with a strike of 30 when the stock is at
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34 could be computed for the shorter time period remaining until expiration. If the
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expected return is negative, an adjustment needs to be made. Adopting this form of
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adjusting would keep the number of trades to a minimum, but would still allow the
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strategist to determine when his position has become improperly balanced. Of
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course, the current volatility would be used in making these determinations. Another |