# Delta: True or False

An increase in the price of the underlying increases delta, so the size of delta hedge call position should be decreased. True or false, and why? Thanks.

Call delta increases when underlying asset increases and delta hedge is devised as the 1/delta, means that hedge ratio decreases, so means you should sell some of your calls in the portfolio to rebalance and maintain an effective hedge.

True, assuming the number of shares doesn’t change. Look at an out-of-the-money call option, as the u/l price moves up the option’s closer to being at-the-money. So the option price will increase at a faster rate, i.e. higher delta. If the delta increases, the number of options has to decrease… because the formula is (# of options) / (#of u/l shares) = -1/delta, or delta*(# of options) = -(# of u/l shares) … so as the delta goes up, # of options goes down.

Thanks. Why call delta increases when underlying asset increases? Delta = Change in option price / Change in stock price. If stock price increases, the denominator increases, then shouldn’t delta decrease?

No, because delta measures the relative rates of change in the option and underlying prices - not absolute change in underlying price

sleepybird Wrote: ------------------------------------------------------- > Thanks. Why call delta increases when underlying > asset increases? > Delta = Change in option price / Change in stock > price. > > If stock price increases, the denominator > increases, then shouldn’t delta decrease? If you were to graph the relationship between the underlying price and the option price, you would see that it is not a linear relationship As a result, as the underlying price moves up or down, the slope of the curved line changes. So at any given point along that curved line, the slope (delta), will change. See exhibit 4 on page 308 of CFAi Volume 5… its shows this graphically. Delta is a similar concept to elasticity in econ. Someone PLEASE tell me if I’m wrong so I can learn it right!!

Thanks. I think I got it. When stock price go up, the denominator goes up, but the numerator also go up at a higher pace. This is because when stock price increase, the value of the calls increases, so does the premium. So overall delta increases. CF-AHHHHHHH Exhibit 4 on page 308 is for delta hedging currency with puts in relation to exchange rate. It looks to me when the underlying exchange rate increase, the slope decreases (flatten), so delta decreases in this case.

Yeah, because a put will react in the opposite direction as a call. The principles of delta remain the same, however. I just thought Exhibit 4 was a good visual aid for the concept… not necessarily your specific question as it pertained to calls.

Is hedge ratio = -1/delta TRUE for both put and call option hedges? The difference is that delta is negative for puts and positive for calls? (put option delta hedge is covered in currency risk hedging)

this kind of questions always get me, because i am always overthinking. for a call option, you need to have positive gamma to have delta and price go the same direction. if they don’t specifically say gamma is positive, i will think the first part of the statement is wrong. i guess cfa pre-assumes it w/o even mention it. but in reality it is not always true. this is why we can do strategies like delta neutral gamma scalping.

lenchik, thats the formula that popped into my head when i saw this question and would have made me answer true… I know for a fact the negative sign represents that you are buying puts, i have assumed up until now if it was positive it means you should buy calls. Not 100% of that last call part tho.

Guys This is pure level II stuff. put delta = call delta -1 for the same strike price, same expiration. - Call delta: 0 for far out of money,1 for far in the money. It moves from 0 to 1 when stock price increases. - Put delta: 0 for far out of money, -1 for far in the money. Moves from -1 to 0 when stock price increases. The hedge ratio = -1/delta applies both call and put. As delta increases for call when stock price up --> 1/delta decreases --> less call needed for hedge. As delta decreases for call when stock price up --> 1/delta increases --> more call needed for hedge. Dust off your level II book, if you are still in doubt.

come on. delta hedge is simply -1/delta. delta up call down. i believe everybody gets this part. what really gets me is underlying price is not relevant here. or i should say not directly related to the hedge. i don’t need it to rebalance a delta hedge. why they throw it in? by saying “An increase in the price of the underlying increases delta, so …” are they implying price increase will definitely lead to delta increase? that’s surely wrong.