I am not challenging the number of the call to be sold as indicated in its solution. Instead, I am challenging that why hedge the $5M FI position by “selling calls”. Is it that hedging by “buying puts” is more appropriate in this case ? Actually by selling calls, it just can cover a small portion of the loss (offset the loss by the premium from selling calls) once the value (price) of the $5M declines while it limits the up-side potential. If the value (price) declines to a great extent, there will be no effectiveness to hedge by “selling calls”. This is just same as the case of selling “covered calls”. Any comment ?

Any comment ?

This is just “my guess” (I don’t have a real-world example)-- Based on his/her interest rate expectation, the mgr. may believe that the possibility of upside movement for the $5Mil bond’s price is very slim within the time-horizon. Within this period, there are some chances of interest rate increase (need some protection) but he/she also forecasts that the interest rate most likely will stay the same (so he can earn the call premium thr. delta hedging). If the mgr. forecasts the interest rate will be volatile during the time-horizon and that is high chance of upside movement on bond price, he may buy puts instead.

James@Houston, Yes, there is no clear scenario description. TKVM ! BTW, is it that earn the call premium through “covered call” shall be correct (you said : thr. delta hedging) ?

One can either use short call or long put, all depending on which derivatives available and what’s their delta. In delta hedging, the point is on hedging SMALL change, Not to make money. If the price changes a lot, delta changes then the hedge will not be effective longer (i.e., one to one hedging), independent whether you are using put or call to hedge -> one needs adjust the number of options to be hedged once delta changes, so called dynamic hedging. To measure this effectiveness of delta hedging, one uses Gamma. In short, one continously monitors the delta as the portfolio shifts and adjusts the number of options, and never let it change a lot as you seem to indicate.

elcfa, TKVM for your response ! Can I conclude as follows ? Covered call : The purpose is to make profit (premium) in an oscillating market. Delta (dynamic) hedging : hedging SMALL change

> Covered call : The purpose is to make profit > (premium) in an oscillating market. Earn premium if price will stay mostly the same (at expiration). This happens most of the time. If one thinks market will have a lot of volatility, so believes price at expiration is widely different from current price --> a straddle is better. If one thinks market will be up by a lot --> just do plain stock. > Delta (dynamic) hedging : hedging SMALL change yes

elcfa, TKVM for your advice for the applications of covered call & delta hedging. BTW, do you have some best ways (short-cuts) to derive those fromula for the options strategies of Bull Call / Bear Put / Butterfly / Straddle / Collar / Box Spread ? I can derive those formula but I am afraid that it will cost me much time to derive those formula and I may make mistakes under the time pressure. Therefore, you will be much appreciated if you can advise me some best ways (short-cuts) which can save me time while no mistake will be made. TKVM for your help again !

Well, not mean to be a rigorous PhD dissertation, but more of quick and dirty short cuts/double checks. Take it for whatever it’s worth. Step 1: draw the chart and position. Covered call: cap/covered at top. Protective put: flat bottom. Spread and collar: flat both. Butterfly spread and straddle: v shaped. Step 2: find initial investment. Spread: buy and sell same instrument at lower price. Butterfly: buy and sell bull spreads. Boxed: bull + bear spread. Straddle: put +call same strike. Collar: (stock +) put – call (normal zero cost -> same price) Step 3: Max profit. For spread: spread – initial cost. Step 4: Max loss: initial investment (except when you also own stock: e.g., covered call, protective put or collar) Step 5: Break-even: The trick here is to look at the line and recognize that the slope of the payoff curve is either 1 or -1, so you either use the value where - The bottom line starts (lower strike price) and add max loss - The top line starts (upper strike price) and subtract max profit. Example: Bull spread: bottom line starts at strike 65. Max loss is 5 break even is 65+5 = 70. Butterfly: Bottom line starts at 130, max loss =1 -> breakeven = 130+1. Collar: Top line starts at strike 50,59, max profit = 8,59 -> breakeven = 50,59 – 8,59= 43 Added bonus: it would give you opportunities to double check whether you have calculated your max profit and loss correctly. For collar, since the collar is zero cost, breakeven is the price of buying stock and max loss/profit is just the spread between breakeven and strike prices. Box spread: payoff always RF (if price correctly)

elcfa, You are very much appreciated. I will try to follow your ways & hope they will minimize my time & mistake. I will come back to you If I have further question. TKVM again !