Greeks Computation for Put Option

The day before yesterday, I posted the computation of the Greeks for call option. In today’s posting, I will continue to discuss how to do the computation of the Greeks for put option (I have purposely waited for two days to do this posting so we can see how the formulas work for us). I have also tried the formulas for the computation of Greeks for put option and compared the results to those on OptionXpress. Well, once again I cannot really say that these formulas gave very good results but they are close enough like in the case of the call option.

I am going to put down the steps for computing the Greeks for put option. You can simply follow through the steps and try out on your own if you are interested. I am going to do the Greeks for put options on the same worksheet that I used yesterday and I am going to list down the step of what you should key in each cell. If you follow exactly the cell reference I am using (which once again, I seriously encourage you to do so if you wish to try out), you should be able to just copy the formulas I have and paste them correctly into the cell reference to get the results. I am also going to include the formulas for computing the put option pricing here as well together with the computation of the Greeks.

Open the same Excel worksheet that we used yesterday, type in the following data;

1. In cell E2 and F2, perform a merge cell and type in “Put Option Pricing”.
2. In cell E3, type in “Stock Symbol”. Again, I am going to use Agilent Technologies as an example; hence I am going to put the symbol “A” in cell F3.
3. In cell E4, type in “Link”. Copy and paste this formula =IF(ISBLANK(F3),"",HYPERLINK("https://www.optionsxpress.com.sg/quote_detail.asp?symbol="&UPPER(F3)&"&SessionID=0",F3)) in cell F4. Hence cell F4 will update every time to provide you with the hyperlink to the stock based on the stock symbol you input in cell F3. You can click on the hyperlink to get the stock information for Agilent Technologies in this case.
4. In cell E5, type in “Stock Option Chains”. Copy and paste this formula =IF(ISBLANK(F3),"",HYPERLINK("https://www.optionsxpress.com.sg/quote_option_chain.asp?SessionID=&symbol="&UPPER(F3)&"&Page=V&lstMarket=0&Range=ALL&AdjNonStdOptions=OFF&lstMonths=13",UPPER(F3)&"'s Option Chain")) in cell F5. Hence cell F5 will update every time to provide you with the hyperlink to the stock option chain based on the stock symbol you input in cell F3. You can click on the hyperlink to get the stock option chain information for Agilent Technologies in this case.
5. In cell E6, type in “Option Symbol”. Type in “AQF” in cell C6. I am going to use the May 08 put option with strike price of USD$30.00 for my illustration purpose.
6. In cell E7, type in “Current Stock Value”. If you have click on the hyperlink in cell F4, you should be able to get the last traded stock price for Agilent Technologies. At this point of writing, the last traded price was USD$29.67. Type in 29.67 (without the dollar sign symbol, you can format it later) in cell C7.
7. In cell E8, type in “Implied Volatility”. If you have click on the hyperlink in cell F5, you should be able to get the option chain for Agilent Technologies. You should be able to find the implied volatility for AQF. At this point of writing, the implied volatility for AQF is 38.1%. Type in 38.1% (including the percentage symbol) in cell F8.
8. In cell E9, copy and paste the following formula: =HYPERLINK("http://cdrates.bankaholic.com/","6-month CD rate (annualized)"). This should provide you with the hyperlink to get the 6-month CD rate (annualized). At this point of writing, due to the recent Fed rate cut, the 6-month CD rate (annualized) is 4.05%. Type in 4.05% (including the percentage symbol) in cell F9.
9. In cell E10, type in “Dividend Payout per Share”. Using the same hyperlink from cell F4, you will realize that Agilent Technologies does not pay out dividend. You should see under the Dividend heading on the website with n/a. Agilent Technologies does not pay out dividend but instead they do stock repurchase from open market. Hence, type in 0 in cell F10 in this case.
10. In cell E11, type in “Days to expiration”. Using the same hyperlink from cell F5 which provides you the link to the option chain for Agilent Technologies, the May 08 put option has another 60 days to expiration. Type in 60 in cell C11.
11. In cell E12, type in “Strike Price”. Again, using the same hyperlink from cell F5, the strike for AQF is USD$30.00. Type in 30 (without the dollar sign symbol, you can format it later) in cell F12.
12. In cell E13, type in “Put Option Price (Approximate)”. Copy and paste the formula =IF(F7<>0,-F7*EXP(-F10/F7*F11/365)*NORMSDIST(-SUM(LN(F7*EXP(-F10/F7*F11/365)/F12),SUM(F9,POWER(F8,2)/2)*F11/365)/(IF(F8=0,0.00000000001,F8)*POWER(F11/365,0.5)))+F12*EXP(-F9*F11/365)*NORMSDIST(-SUM(LN(F7*EXP(-F10/F7*F11/365)/F12),SUM(F9,POWER(F8,2)/2)*F11/365)/(IF(F8=0,0.00000000001,F8)*POWER(F11/365,0.5))+F8*POWER(F11/365,0.5)),0) in cell F13. You should get a value of USD$1.897. This is the theoretical value for the put option for AQF. At point of writing the bid-ask prices for AQF are USD$1.92 and USD$1.96 respectively. The last traded price was USD$1.85.
13. I now move on to do the computation for this put option Greeks. The formula I am going to show may appear very complicated. The good thing is, you can just copy and paste them to your cell reference. I have done the tough portion for you. In cell E15, type in “Delta”. Copy and paste the following formula =NORMSDIST((LOG(F7/F12)+F11/365*(F9+0.5*F8^2))/(F8*SQRT(F11/365)))-1 in cell F15. You should get a value of -0.464. Using the link from step four, navigate to the top of the website and change the "Type" to "Pricer" and "Expiration" to "May 08" and click the "View Chain" button to get the Greeks for AQF. You need to select the “Puts” radio button too. Change the various values on the website and click on calculate. For example, in the “Current Imp Vol”, you should change to 38.1%. In the “Days Until Exp”, you should change to 60. Lastly, in the “Int Rate”, you should change the value to 4.05%. Click on the calculate button and you should get the Greeks value for all the May 08 put option updated. Leave this page as it is as we will be comparing the remaining values later. Note that the delta is -0.487 and the “Theo Value” (which is the theoretical value for the call option price) is 1.919.
14. Let’s move on to do the computation for the remaining Greeks. In cell E16, type in “Gamma”. Copy and paste the following formula =EXP(-((LOG(F7/F12)+F11/365*(F9+0.5*F8^2))/(F8*SQRT(F11/365)))^2/2)/SQRT(2*PI())/F7/F8/SQRT(F11/365) in cell F16. You should get a value of 0.087. The Gamma value on the website from step 13 is 0.091.
15. In cell E17, type in “Vega”. Copy and paste the following formula =F7*EXP(-((LOG(F7/F12)+F11/365*(F9+0.5*F8^2))/(F8*SQRT(F11/365)))^2/2)/SQRT(2*PI())*SQRT(F11/365)/100 in cell F17. You should get a value of 0.048. Again the Vega value on the website from step 13 is 0.048.
16. In cell E18, type in “Theta”. Copy and paste the following formula =(-F7*EXP(-((LOG(F7/F12)+F11/365*(F9+0.5*F8^2))/(F8*SQRT(F11/365)))^2/2)/SQRT(2*PI())*F8/2/SQRT(F11/365)+F9*F12*EXP(-F9*F11/365)*NORMSDIST(F8*SQRT(F11/365)-((LOG(F7/F12)+F11/365*(F9+0.5*F8^2))/(F8*SQRT(F11/365)))))/365 in cell F18. You should get a value of -0.014. The Theta value on the website from step 13 is -0.014.
17. Lastly, let compute the “Rho”. In cell E19, type in “Rho”. Copy and paste the following formula =-F11/365*F12*EXP(-F9*F11/365)*NORMSDIST(F8*SQRT(F11/365)-((LOG(F7/F12)+F11/365*(F9+0.5*F8^2))/(F8*SQRT(F11/365))))/100 in cell F19. You should get a value of -0.026. The Rho value on the website from step 13 is -0.027.

Once again I really hope you all enjoy this as much as I do. I hope this modeling can help you in better choosing your option in future.

Greeks Computation for Call Option

The beginning of March 2008 is a wonderful day for my family. On 1st March, my nephew had finally arrived to this world. This is really a happy occasion for my whole family. The first week of March was also my last two lessons for the Wealth Academy Trader tutorial. Unfortunately, I fell sick and I missed my fourth lesson which Conrad taught about his 5DPEG. I heard from my course mates that that the lesson was one of the most interesting of all. I am now waiting anxiously for my makeup lesson in April.

Nevertheless, I did attend the last lesson and Lawrence taught about option trading. I have some basic knowledge about option trading and its Greeks. The thing that I am not too sure is how do I make use of the Greeks? I have been waiting for this lesson to learn on the interpretation of the Greeks and most importantly, their applications. Lawrence illustrated the usage of the Greeks with examples and this has really intrigued me. My first thought in my head was then how can I compute the Greeks myself and how can I apply them to warrant trading? The next thing I was asking myself is the relationship between historical and implied volatility. I have figured out how I can compute the historical and implied volatility but I do not know if there is a relationship between them?

I actually went on to do my own research on the computation of the Greeks and the relationship between historical and implied volatility. Well, my hard work did pay off and I manage to find the ways to compute the Greeks but unfortunately, the relationship between historical and implied volatility is not so straight forward and it required the understanding of regression model to understand how the relationship is being model. Furthermore, I believe the parameters to the model have to be tuned and changed accordingly as time goes by and whenever the underlying of the model is changed. As such, I decided to post my finding of the computation of the Greeks which can be easily done using Microsoft Excel.

I have tried the formulas for the computation of Greeks and compared the results to those on OptionXpress. Well, I cannot really said that these formulas gave very good results as compared with my previous posting of option pricing using the Black Scholes formula but at times they gave very close estimates. I have been trying to figure out how can I use these same formulas to compute the Greeks for warrant trading? This is because information on warrant Greeks is not so easily available as compared with option. Sad to say, I did not succeed. My original intention was to blog on how we can compute the Greeks for warrant? This also explains why I have not been blogging for so long. Hence I decided that I should post my finding on the computation of the Greeks for option and perhaps some of my readers can go ahead and figure out how to do so for warrant and it would be great if he or she can share the finding with us.

I am going to put down the steps for computing the Greeks for option. You can simply follow through the steps and try out on your own if you are interested. I am going to do both the Greeks for call and put options on the same worksheet and I am going to list down the step of what you should key in each cell. If you follow exactly the cell reference I am using (which I seriously encourage you to do so if you wish to try out), you should be able to just copy the formulas I have and paste them correctly into the cell reference to get the results. I am also going to include the formulas for computing the option pricing here together with the computation of the Greeks.

I will start doing with the Call option first and later for the Put option in another posting. Open an Excel workbook and on one of the worksheets, type in the following data;

1. In cell B2 and C2, perform a merge cell and type in “Call Option Pricing”.
2. In cell B3, type in “Stock Symbol”. I am going to use Agilent Technologies as an example; hence I am going to put the symbol “A” in cell C3.
3. In cell B4, type in “Link”. Copy and paste this formula =IF(ISBLANK(C3),"",HYPERLINK("https://www.optionsxpress.com.sg/quote_detail.asp?symbol="&UPPER(C3)&"&SessionID=0",C3)) in cell C4. Hence cell C4 will update every time to provide you with the hyperlink to the stock based on the stock symbol you input in cell C3. You can click on the hyperlink to get the stock information for Agilent Technologies in this case.
4. In cell B5, type in “Stock Option Chains”. Copy and paste this formula =IF(ISBLANK(C3),"",HYPERLINK("https://www.optionsxpress.com.sg/quote_option_chain.asp?SessionID=&symbol="&UPPER(C3)&"&Page=V&lstMarket=0&Range=ALL&AdjNonStdOptions=OFF&lstMonths=13",UPPER(C3)&"'s Option Chain")) in cell C5. Hence cell C5 will update every time to provide you with the hyperlink to the stock option chain based on the stock symbol you input in cell C3. You can click on the hyperlink to get the stock option chain information for Agilent Technologies in this case.
5. In cell B6, type in “Option Symbol”. Type in “AEF” in cell C6. I am going to use the May 08 call option with strike price of USD$30.00 for my illustration purpose.
6. In cell B7, type in “Current Stock Value”. If you have click on the hyperlink in cell C4, you should be able to get the last traded stock price for Agilent Technologies. At this point of writing, the last traded price was USD$29.64. Type in 29.64 (without the dollar sign symbol, you can format it later) in cell C7.
7. In cell B8, type in “Implied Volatility”. If you have click on the hyperlink in cell C5, you should be able to get the option chain for Agilent Technologies. You should be able to find the implied volatility for AEF. At this point of writing, the implied volatility for AEF is 36.9%. Type in 36.9% (including the percentage symbol) in cell C8.
8. In cell B9, copy and paste the following formula: =HYPERLINK("http://cdrates.bankaholic.com/","6-month CD rate (annualized)"). This should provide you with the hyperlink to get the 6-month CD rate (annualized). At this point of writing, due to the recent Fed rate cut, the 6-month CD rate (annualized) is 4.05%. Type in 4.05% (including the percentage symbol) in cell C9.
9. In cell B10, type in “Dividend Payout per Share”. Using the same hyperlink from cell C4, you will realize that Agilent Technologies does not pay out dividend. You should see under the Dividend heading on the website with n/a. Agilent Technologies does not pay out dividend but instead they do stock repurchase from open market. Hence, type in 0 in cell C10 in this case.
10. In cell B11, type in “Days to expiration”. Using the same hyperlink from cell C5 which provides you the link to the option chain for Agilent Technologies, the May 08 call option has another 62 days to expiration. Type in 62 in cell C11.
11. In cell B12, type in “Strike Price”. Again, using the same hyperlink from cell C5, the strike for AEF is USD$30.00. Type in 30 (without the dollar sign symbol, you can format it later) in cell C12.
12. In cell B13, type in “Call Option Price (Approximate)”. Copy and paste the formula =IF(C7<>0,C7*EXP(-C10/C7*C11/365)*NORMSDIST(SUM(LN(C7*EXP(-C10/C7*C11/365)/C12),SUM(C9,POWER(C8,2)/2)*C11/365)/(IF(C8=0,0.00000000001,C8)*POWER(C11/365,0.5)))-C12*EXP(-C9*C11/365)*NORMSDIST(SUM(LN(C7*EXP(-C10/C7*C11/365)/C12),SUM(C9,POWER(C8,2)/2)*C11/365)/(IF(C8=0,0.00000000001,C8)*POWER(C11/365,0.5))-C8*POWER(C11/365,0.5)),0) in cell C13. You should get a value of USD$1.725. This is the theoretical value for the call option for AEF. At point of writing the bid-ask prices for AEF are USD$1.64 and USD$1.77 respectively. The last traded price was USD$1.73.
13. I now move on to do the computation for this call option Greeks. The formula I am going to show may appear very complicated. The good thing is, you can just copy and paste them to your cell reference. I have done the tough portion for you. In cell B15, type in “Delta”. Copy and paste the following formula =NORMSDIST((LOG(C7/C12)+C11/365*(C9+0.5*C8^2))/(C8*SQRT(C11/365))) in cell C15. You should get a value of 0.535. Using the link from step four, navigate to the top of the website and change the "Type" to "Pricer" and "Expiration" to "May 08" and click the "View Chain" button to get the Greeks for AEF. Change the various values on the website and click on the "Calculate" button. For example, in the “Current Imp Vol”, you should change to 36.9%. In the “Days Until Exp”, you should change to 62. Lastly, in the “Int Rate”, you should change the value to 4.05%. Click on the "Calculate" button and you should get the Greeks value for all the May 08 call option updated. Leave this page as it is as we will be comparing the remaining values later. Note that the delta is 0.517 and the “Theo Value” (which is the theoretical value for the call option price) is 1.729.
14. Let’s move on to do the computation for the remaining Greeks. In cell B16, type in “Gamma”. Copy and paste the following formula =EXP(-((LOG(C7/C12)+C11/365*(C9+0.5*C8^2))/(C8*SQRT(C11/365)))^2/2)/SQRT(2*PI())/C7/C8/SQRT(C11/365) in cell C16. You should get a value of 0.089. The Gamma value on the website from step 13 is 0.091.
15. In cell B17, type in “Vega”. Copy and paste the following formula =C7*EXP(-((LOG(C7/C12)+C11/365*(C9+0.5*C8^2))/(C8*SQRT(C11/365)))^2/2)/SQRT(2*PI())*SQRT(C11/365)/100 in cell C17. You should get a value of 0.049. Again the Vega value on the website from step 13 is 0.049.
16. In cell B18, type in “Theta”. Copy and paste the following formula =(-C7*EXP(-((LOG(C7/C12)+C11/365*(C9+0.5*C8^2))/(C8*SQRT(C11/365)))^2/2)/SQRT(2*PI())*C8/2/SQRT(C11/365)-C9*C12*EXP(-C9*C11/365)*NORMSDIST(((LOG(C7/C12)+C11/365*(C9+0.5*C8^2))/(C8*SQRT(C11/365)))-C8*SQRT(C11/365)))/365 in cell C18. You should get a value of -0.016. The Theta value on the website from step 13 is -0.016.
17. Lastly, let compute the “Rho”. In cell B19, type in “Rho”. Copy and paste the following formula =C11/365*C12*EXP(-C9*C11/365)*NORMSDIST(((LOG(C7/C12)+C11/365*(C9+0.5*C8^2))/(C8*SQRT(C11/365)))-C8*SQRT(C11/365))/100 in cell C19. You should get a value of 0.024. The Rho value on the website from step 13 is 0.023.

I hope you all enjoy this as much as I do. Please do not delete away the spreadsheet as I will use the same one to illustrate the computation for the put option in my later post. For those who understand and trade options and warrants, you will appreciate more and how this modeling exercise can help you better in choosing your option.

Analysis of Warrant Data (Part 8)

Today is the 29th of February 2008. I suppose you know this day only comes once every four years. This year is a leap year. I am not too sure if you know there is also something known as the leap century which occurs once every four hundred years. Something interesting about the leap century is that the 1st of January of a leap century always falls on a Saturday. You can easily verify this with a perpetual calendar if you are interested. The last leap year was 2004 and the last leap century was 2000. We have to wait for another four years till 2012 for another leap year and 2400 for another leap century. I do not think I will see that year coming.

Theta

In warrant, there is the effect of time as well and you do not have the luxury of another four years. The Greek used to measure time is known as theta. Theta, also called time decay, measures the rate of change in the price of a warrant as its maturity is running short while all other things being equal. It can be expressed as an absolute value or a percentage relative to the warrant price (theta / warrant price). Unless in some special circumstances, the value of theta is usually negative, reflecting the declining value of a warrant as time passes. The time decay has its greatest effect when the warrant is near to its maturity. Time decay accelerates as time passes.

In percentage terms, time value has the biggest impact on out-of-the-money (OTM) warrants. The value of a warrant consists of intrinsic value and time value. They vary in absolute and relative terms for warrants with different strike prices and maturity dates. In the case of OTM warrants, their intrinsic values are negligible or zero. In other words, time value makes up most of their values. Hence, they are more sensitive to the passage of time. As for the in-the-money (ITM) warrants, given that a large part of their value is made up of intrinsic value, they are less sensitive to the passage of time, and such sensitivity decreases as the maturity date gets nearer.

Investors should find out more about the theta of a warrant as a percentage relative to its price, that is, relative theta. The latter is a better indicator to the sensitivity of a warrant to the passage of time, and will give you a better idea about the effect of time value on the gain or loss on warrants you are holding.

Vega

Vega measures the rate of change in the warrant price for each point of movement of its implied volatility. No matter it is a call warrant or a put warrant, Vega is always positive, indicating that the warrant price and its implied volatility always move in the same direction. Vega can be an absolute value or a percentage relative to the warrant price.

In terms of the percentage change in price, changes in implied volatility have the biggest impact on OTM warrants. Besides, the closer they get to the maturity, the bigger the impact. Next come at-the-money (ATM) warrants, and then ITM warrants. For the latter, the closer they get to maturity, the smaller the impact. Hence, in picking warrant, investors should check out its Vega as a percentage relative to change in warrant price, in order to assess the impact of implied volatility on the warrant.

Gamma

Gamma measures the sensitivity of the delta of a warrant to the price movements of its underlying. The higher the gamma, the bigger the change in delta will be in reaction to a movement in the underlying price.

Gamma = rate of change of delta / rate of change of underlying price

No matter it is a call warrant or put warrant, gamma is always positive. When the underlying goes up, in the case of a call warrant, its delta will go up as it is more likely to be ITM; in the case of a put warrant, the same will happen too as it is more likely to be OTM and its delta will get closer to zero.

ATM warrants (for those with maturity of less than a year) have the highest gamma. This means that they have the highest rate of change of delta.

Rho

Rho measures the sensitivity of warrant price to changes in the market interest rate. Call warrants have a positive rho, meaning that the price of a call warrant moves in the same direction as the market interest rate. In contrast, put warrants have a negative rho, and this shows that the price of a put warrant moves in the opposite direction to the market interest rate. Given that changes in interest rates tend to be limited in the short term, their effect on warrant prices is minimal.

This is my last post on analysis of warrant data. What I have discussed above is known as the Greeks of warrant. They look quite similar to those of option. The Greeks are important in trading both warrants and options. Unfortunately, the information for the Greeks for warrants are not easily available as compared with options.

Analysis of Warrant Data (Part 7)

I went for a MSDN Tech-Talk held by Microsoft yesterday at One Marina Boulevard in the NTUC Auditorium. I was particularly impressed by the SQL Server 2008 that is going to be release soon in March. There is this Data analysis feature available since SQL Server 2005 and this is really a very powerful feature I would say. You can download a plug-in for Microsoft Excel 2007 and made used of this data analysis feature that comes with the developer, standard and enterprise version of the SQL Server 2005 and 2008 to perform time series regression to forecast short term and long term trend of data available in either the SQL Server or Microsoft Excel 2007. The plug-in also allows you to generate a report formatted with visual cue that made interpreting the data much easier.

I will be testing out the feature once I can get the SQL Server analysis service to setup on my computer. Meanwhile in today’s posting, I am going to continue on the Analysis of warrant data. I have been busy preparing my CFA level II examination and hence have not been updating my blog as regularly. This is the second last post on Analysis of warrant data which I will talk about Delta.

Put simply, delta measures how much, in theory, the warrant price will move for a $1.00 change in the underlying price (For me, I treat this as the first derivative of warrant price, typical engineer thought). For investors, delta is meaningful in the following aspects:

Relationship between delta and ITM/ATM/OTM

Call warrants have a positive delta, which means that the underlying price and the warrant price move in the same direction. On contrary, put warrants have a negative delta, which means that the underlying price and the warrant price move in opposite direction.

The value of delta lies between 0 and 1 for a call warrant, and between 0 and -1 for a put warrant. When a call warrant is at-the-money (ATM), its delta should be around 0.5. This value will move closer to 1 in the case the warrant becomes deeper in-the-money (ITM), or closer to 0 in the case the warrant moves further out-of-the-money (OTM). For a put warrant, when it is ATM, its delta should be around -0.5. Likewise, this value will move closer to -1 in case the warrant becomes deeper ITM or closer to 0 in case the warrant moves further OTM.

Delta reflects the degree of probability that a warrant will be ITM at maturity. A far OTM warrant has a delta close to 0, indicating almost zero chance that it will become ITM at maturity. An ATM warrant has a delta of around 0.5 and there is about 50% chance that the warrant will become ITM at maturity. A deep ITM warrant has a delta close to 100%, and this means there is nearly 100% chance that the warrant will stay ITM at maturity.

Prediction of changes in the warrant price

In general, investors can use delta to predict how much the warrant is likely to move for a $1.00 change in the underlying price. Say, for example, UOB BNP ECW100319 has a delta of 0.7468 after market closed yesterday. The conversion ratio is 14.993. The closing price for UOB was $18.42 yesterday. If the underlying price goes up by $1.00, the warrant price should, in theory, rise by $1.00 * 0.7468 / 14.993 = $0.05.

In reality, when the underlying price goes up or down by $1.00, the warrant is unlikely to move by the exact amount suggested by its delta, which is not a constant, but a variable. It will vary along with the underlying price, implied volatility and days to maturity. For example, assuming that the underlying price remains constant, with its time value or implied volatility falling, an OTM warrant will see a decline in its delta while an ITM warrant will see a rise. Usually, investors focus only on the relationship between delta and changes in the underlying price, and neglect the effect of changes in the implied volatility and time value.

Besides, the price of a warrant is determined by the market, and will be affected by market sentiments, market making activities, and the outstanding quantity of warrant. Hence, warrant usually trade at a level different from the theoretical price suggested by its delta.

Finding out the number of units of the warrant to be bought

Investors can also use delta to roughly estimate how many units of a warrant should be bought to reap a potential return close to that from a given units of the underlying. For example, a certain investor is optimistic about the UOB counter and wants to invest with a smaller amount of capital. If the investor wants to get an exposure to 1000 shares of UOB stock, using the previous warrant as an example, the delta is 0.7468, the number of units of warrant the investor should buy is equal to 1000 (the number of shares) divided by 0.7468 (the delta of the warrant), that is, 1340 units.

Finding out the number of units of new warrant to be bought for switching

Besides, investors can also use delta to roughly estimate how many units of a warrant need to be bought for switching to maintain the potential return. If the warrant on hand is about to expire or is going further OTM, one should consider switching. To find out how to use delta to calculate the number of units of the new warrant that need to be bought to replace the old warrant in order to maintain potential return at the original level, we can simply divide the delta of the warrant we intend to switch with that of the warrant we are switching to.

For example, CAPITALAND DB ECW080616 and CAPITALAND DB ECW080616 A have a strike of $7.30 and $6.30 respectively. Both have a conversion ratio of 5:1 and same maturity date. At point of writing, CapitaLand has a price of $6.62. Hence CAPITALAND DB ECW080616 A is ITM and CAPITALAND DB ECW080616 is OTM. CAPITALAND DB ECW080616 A has a delta of 63.27% and an effective gearing of 5.08x while CAPITALAND DB ECW080616 has a delta of 43.11% and an effective gearing of 5.44x. We noticed that CapitaLand share price has been going up for at least the past two weeks and says we remain positive that CapitaLand will move further up in price for next two weeks. Hence we want to switch from CAPITALAND DB ECW080616 A to CAPITALAND DB ECW080616 since it has a higher effective gearing even though CAPITALAND DB ECW080616 A has a higher delta. Therefore, we need to buy 63.27/43.11 = 1.46 units of CAPITALAND DB ECW080616 for each unit of CAPITALAND DB ECW080616 A to maintain the potential return.

You may ask, since the potential profit remains more or less the same, why should be bothered with switching at all? Why should we pay the additional transaction costs for selling CAPITALAND DB ECW080616 A and buying CAPITALAND DB ECW080616?

The purpose of switching is to allow us to sell a warrant with a higher price for another warrant with a higher effective gearing so as to invest with less capital for better utilization of funds. We do not have to be bound by the switching ratio, but it will give us an idea about how many units of new warrant we should buy to maintain potential profit as the same level.

The examples given are for illustration purpose and not my recommendation. I have tried to use real examples to illustrate my points. I will be positing my last post on analysis of warrant data soon.

A New Way to Value the Market

I came across this article by Geoff Colvin, senior editor from Fortune magazine, and I thought it is an interesting article to share with my readers. The article discussed about the valuation of company using the economic value added (EVA). I have reposted the article in my blog here for your reading.

Are stocks cheap yet? That slippery, eternal question is worth a look right now because a remarkable new set of data has just become available, allowing us to analyze the market in ways we never could before. I wish I could tell you that this new trove of numbers reveals that stocks are a screaming buy. It doesn't. But it does suggest that, amid all the recent tumult, just maybe the market is being rational.

The new data are derived from the most fundamental, capital-based way of analyzing a company's finances and value. How much capital is a company using? What is its return on capital? How much does the capital cost? Those questions hold the key to corporate performance, but finding the answers in most financial statements isn't easy, and many executives don't know the answers themselves. The Stern Stewart consulting firm began popularizing these concepts more than 15 years ago with the term EVA (economic value added), and the new data come from EVA Dimensions, a firm that is now the source of Stern Stewart's EVA data.

EVA-based analysis has proven extremely valuable in analyzing individual companies. I almost never make calls on specific stocks, but in late 1999 the EVA analysis of AOL was so compelling that I wrote a column declaring flatly that the stock price could not possibly be justified. That column was published on Jan. 10, 2000, right near the overall market peak (and the very day that AOL announced it was using its insanely overvalued stock to buy my employer, Time Warner (TWX, Fortune 500) - but that's another story). I also used EVA analysis to write last summer that Google (GOOGLE) was overpriced at $540; that call looked wrong for a while, though as I write this the stock is at $501.

One thing you couldn't do with EVA analysis was use it to value the whole market. Compiling the data for a significant number of companies used to take months. But now, through the miracles of our networked world, EVA Dimensions can compile it every day for 2,669 companies in the Russell 3000 (those for which at least two years of data are available). This is essentially the U.S. stock market. So: Is it worth what it costs?

Look first at how well the companies are doing at their most basic task, which is earning a return on their capital that's greater than the total cost of that capital. Turns out they've been doing very well. The dollar difference between their return on capital and cost of capital (their EVA) was $375 billion over the past four quarters. It was only half that much in 2005, and in 2004 it was negative, which isn't surprising. Over time, for the broader market, EVA should be more or less zero since competition is always forcing high returns down toward the cost of capital, while companies that can't meet their capital cost will eventually go under. So America's publicly traded companies did great last year; in fact, with economic growth strong through the third quarter, it's safe to say that they were at or near the top of the business cycle.

Next question: How are they being valued? On a recent day when the Dow closed at 12,265, the 2,669 Russell 3000 companies had a total enterprise value of $29.8 trillion (equity plus debt). To judge whether that's a lot or a little, consider that over the past four quarters these companies produced after-tax operating profits of about $1.8 trillion. Even if we assume that earnings will only match, not exceed, that level in future years, then the companies' aggregate market value today would still be $22.5 trillion (note to finance wonks: that's their profits capitalized at their capital cost of about 8.1%), which is about 75% of their actual market value.

So now we reach the central question. About 25% of the current market value of these companies is based on expectations of future profits above and beyond the profits they earned last year, at the top of the business cycle. Does that seem reasonable? Actually, it just might. The math gets a bit tedious, but you can assume no profit growth for the next several years and very modest growth thereafter, and the valuation still looks okay. Buying at today's prices may not make you rich. But - for the first time in a long time, in my view - it isn't crazy.

Analysis of Warrant Data (Part 6)

Time really flies. Today is the 7th day of Chinese Lunar New Year also known as 人日, which means it is the birthday of human beings. Therefore, I would like to wish everyone a happy birthday. This is part 6 of my posting on Analysis of Warrant Data. In this post I will talk about effective gearing and gearing.

The biggest appeal of warrant trading lies in the leverage effect. Investors only need to invest a small sum to earn a potential return or even higher than that from directly investing in the underlying. However, in picking warrant, investors often get confused with gearing and effective gearing. So, what are the differences between them? Which of them is more indicative?

Gearing

Gearing only reflects how many times the underlying costs versus the warrant. Its calculation formula is:

Gearing = Underlying Price / (Warrant Price * Conversion Ratio)

For example, the SPC call warrant, SPC RB ECW080526, has a gearing of 7.12 times at point of writing. Then an investment of S$1000 for the warrant will be equivalent to an investment of S$1000 * 7.12 = S$7120 in the underlying. However, gearing do not reflect the relationship between changes in the warrant price and in the underlying price. For example, both CAPITALAND MBL ECW080606 and CAPITALAND BNP ECW080606 have the same maturity on 6th Jun 2008, same entitlement ratio of 3:1 and approximately same implied volatility 44.65% and 46.17% respectively (I know the implied volatility is not really very close but this pair of warrant is one of the closest I can find to illustrate the effect of gearing).The strike price for the warrants are S$5.80 and S$5.98 respectively. The underlying price at point of writing is S$5.85. We can see that the warrant which is further out-of-the-money has a higher gearing of 10.54x compared with 9.51x. If an investor uses the gearing of these two warrants to work out their potential returns, they may be disappointed. The rate of increase/decrease in the warrant price relative to the underlying price is not the same as gearing. When the underlying price increases by 1%, CAPITALAND MBL ECW080606 with a gearing of 9.51x should ideally increase by 9.51% and CAPITALAND BNP ECW080606 with a gearing of 10.54x should ideally increase by 10.54% too. However, in reality, based on the data I have collected for the two warrants, CAPITALAND MBL ECW080606 increases by 20.59% while CAPITALAND BNP ECW080606 does not move a bid with the same price change movement in the underlying. We should look at the effective gearing.

Effective Gearing

Effective gearing reflects the relationship between changes in the warrant price and in the underlying price. Its calculation formula is:

Effective Gearing = Gearing * Delta

In the example I have chosen above, CAPITALAND MBL ECW080606 has an effective gearing of 5.42x while CAPITALAND BNP ECW080606 has an effective gearing of 5.52x. Then, other things being equal, for every 1% change in the underlying price, the warrant price will in theory move by 5.42% and 5.52% respectively. In my not so perfect example here, because the implied volatility for both warrants are difference which causes the warrant prices to be difference and hence the difference in Effective Gearing. In conclusion, when you invest in warrants, you should look to their effective gearing, not gearing, as a reference for their risk/return performance. Just remember that a high effective gearing can give you a higher leverage but it also means it will fall faster too when the market is in not in favor of your direction of your warrant.

Relationship between maturity and effective gearing

Maturity is negatively related to effective gearing. If we have two warrants with the same strike price but different maturity dates, the one with a longer maturity has a lower effective gearing than the other. This is because that the one with a shorter maturity has a lower time value, and thus a higher effective gearing.

ITM/OTM and effective gearing

Further OTM warrants have a higher effective gearing, because their gearing levels are higher. So, if we have two call warrants with the same maturity but different strike prices, the further OTM one will have a higher effective gearing.

One point that must be stressed here is that although the leverage effect is the biggest appeal of warrants as an investment instrument, one should never blindly go after high returns. While it is true that, generally, a higher effective gearing means a higher potential return, if you are too eager to chase after those OTM warrants which are about to expire, the risk involved can be unaffordable.

These warrants are usually less than one month away from maturity, with an over 10% gap between the strike price and the underlying price, which is extremely out of the money.

By now, most readers must have understood that one should look to the effective gearing to predict the size of change in the warrant price for every 1% change in the underlying price.

Yet, one should note that effective gearing can only reflect the theoretical change in the warrant price in response to a given amount of change in the underlying price in the near term. In fact, when the underlying price changes, the delta and gearing levels will change to, which in turn affect the effective gearing. Besides, the formula for effective gearing is based on the assumption that all other things being equal (such as implied volatility, interest rate and market supply and demand). Hence, in case these factors vary, the warrant price may fail to rise in the way suggested by the effective gearing even in the short term.

In general, premium and effective gearing go up and down together. So, a low-premium warrant has a low effective gearing, and the same goes for the opposite. In the case of a short term ITM warrant, although it carries a high delta, its effective gearing is low due to the high price tag and thus, a low gearing. Mind you, warrant trading is mainly about the leverage effect. When the effective gearing is too low, it does not mean much to invest in the warrant, which only gives you a slightly enlarged return when the underlying price moves. Yet, you are not facing less risk associated with the shortening maturity and changes in implied volatility. The risk and return are out of proportion. Besides, although such warrants have a low premium, they are not suitable for investors with a short term perspective. For a more appropriate strategy, you should first identify your target underlying and short list the relevant warrants with a comfortable effective gearing. Then, simply compare the candidates based on their implied volatility to select your right warrant.

I have been very busy this Chinese Lunar New Year and is unable to blog that regularly. I will be posting more regularly on my upcoming posts. :)

Analysis of Warrant Data (Part 5)

Hi my readers, I am sorry for not posting for awhile. I have been busy doing spring cleaning :) Now my room has once again regained its cleanliness. I am going to continue my posting on analysis of warrant.

There was an article on My Paper on the 1st of Feb 2008, which was last week, regarding option trading. I am not too sure if anyone had read about the article? In the article, there was a short mentioned about the yield curve, a methodology to peek where our economy is heading towards to in year 2008 and perhaps the next one to two years to come. In fact, last year November, I had a similar post to explain the shapes of the yield curves and its implication on the economy. That was one of the reasons I started to monitor the STI put warrants since beginning this year, but I did not trade any of them, at least not using real money. :(

Anyway, I am a novice and risk adverse investor and I do not want to jump straight into the market before I understand how warrants work for me. It is like learning how to drive. We all started on circuit then we moved on to the roads and once we are familiar with it, we can drive safely on roads. Thought that does not guarantee you will not meet up with any accidents (touch wood) but at least you are more cautious and know what to look out for. Hence I do encourage novice investors and traders who wish to trade warrants or stocks to start doing virtual trade and make it as real as possible. Once you are able to reap consistent profit from your virtual trading, then perhaps it is time for you to test out your concepts and skills in the real market. Just remember to minimize your losses and let your profits run.

I would like to continue to share what I have learnt so far in warrant trading. This post is about premium. Premium is a measure of how much the underlying price has to move for the warrant to break even if it is held to maturity.

The premium for a call warrant =

([Strike Price + Warrant Price * Conversion Ratio] – Underlying Price) / Underlying Price * 100%

Whereas, Warrant Price * Conversion Ratio is the cost of buying a warrant, and Strike Price + Cost component is the breakeven point of the warrant. In this formula, we first calculate the difference between the breakeven point and the underlying price and then divide it by the underlying price to find out the premium as a percentage.

Likewise, the premium for a put warrant =

(Underlying Price - [Strike Price - Warrant Price * Conversion Ratio]) / Underlying Price * 100%

For example, the recently listed UOB call warrant UOB BNP ECW100319 is trading at SGD$0.315 at point of writing, with strike of SGD$15.38 and a conversion ratio of 14.993:1. The underlying price is SGD$17.36 at point of writing, then the premium is

Premium = (S$15.38 + S$0.315 * 14.993 - S$17.36) / S$17.36 * 100% = 15.80%
Breakeven = S$15.38 + S$0.315 * 14.993 - S$17.36 = S$20.10

In other words, if the investor intends to hold the warrant until maturity, its takes 15.8% increase in the underlying price from its current level of S$17.36 to S$20.10 to breakeven. In this example, what we have is an in-the-money (ITM) warrant, and the underlying needs a modest increase in the underlying price to breakeven. In the case of an out-of-the-money (OTM) warrant, the underlying must make a bigger climb to reach the breakeven point.

To sum up, the premium only measures the percentage increase in the underlying price that will allow the warrant investor to breakeven upon maturity. It does not tell us whether the price of a warrant is too high or too low. Hence, unless you are prepared to hold the warrant until maturity, premium is not a relevant indicator for you.

Today is Lunar New Year eve, I hereby wish everyone 恭喜发财,万事如意.