# Variance swap

Hi!
Newbie here. Can someone please help me to understand why we take off “%” of all the calculations for variance swap. See the attached example from Kaplan notes. If we use the actual volatility figure as given, such as 20%, 21%, and 22%. The expected payoff at maturity should be $1,293.75, right? Two decimals difference/smaller. Can anyone help plsssss? Many thanks!! Much appreciated! Variance Swap|690x307 It must be just the convention for variance swaps. Unfortunately, finance types often drop percent signs when they do calculations, which I find quite revolting (and prone to stupid errors). It appears that this is a case where that’s been codified. The curriculum has this sentence: “[T]he vega notional represents the average profit and loss of the variance swap for a 1% change in volatility from the strike.” However, by a “1% change in volatility”, they mean a change of 0.01 in the variance. Finance people can do really stupid things sometimes. Perhaps you should contact CFA Institute (using this form) and ask them. 1 Like Still kinda confused. I’ve also asked Mark Meldrum as well on his website. I’m curious to see how he responds if he does… Appreciate your reply! Maybe I’ll contact CFAI too! Please let us know what you find out, if anything. MM responded to my question : ‘This is the way it is done. They enter as percent, not decimal. So 16% is just 16, not 0.16.’ I guess you are right. Just the convention for variance swaps…! It is just the scaling factor (10,000) to express Realized Variance in annual basis points (1 bps = 0.01%). => [(0.045175 x 10,000) - (0.04 x 10,000)] = [451.75 - 400] Good morning! Thanks for your reply Pyng. I get the scaling factor (10,000) for the realized variance. But when they calculate variance notional using Vega notional, it was divided by 2K(it’s not the same scaling factor here). See the attached. Using 20%, Variance notional = 250,000. So the result would be: [(0.045175 x 10,000) - (0.04 x 10,000)] x$250,000 = $1,293.75 It’s a different outcome, isn’t it? I get your point. Let’s look at it this way. The notional is specified in volatility terms which means$100K per vega. The variance units is approximate Vega Notional divided by 2 x Volatility strike. Because of this, you have already converted the Variance Notional from Vega Notional. In this case, the variance notional is $100K/(2x20) =$2,500.

=> Variance = 400, therefore, Volatility is = {\sqrt{400}} which is 20. This is consistent to the formula. (Don’t look at it in percentage and convert it to 0.2, otherwise you will be confused)

P.S. The notional amount of a variance swap is scaled from the notional amount of a vega volatility.

Yes, i get it. When variance = 400. Volatility must be 20. LOL
Just whyyyy can’t I look at it in percentage like everywhere else in the book?

Put it this way. If I owe you $3 (=300%), I am not willing to take the % off bc I would owe you$300…lol

Haha. I like that. Okay, if you want to look at it in percentage then I’ll show you here:

=> (0.045175 - 0.04) x 25,000,000 = 129,375

Where 25M = 2,500 x 10,000

Remember as I stated above $100K per vega So, by using the same scaling factor which is 10,000 => [(0.045175 x 10,000) - (0.04 x 10,000)] x 25M/10,000 = 129,375 Hope this helps. I dont get this: Where 25M = 2,500 x 10,000 Shouldn’t you x 100? Thanks for trying to help. • Volatility : 100 bps = 1% • Variance : (100 bps)^2 = (1%)^2 Therefore, 10,000 = 0.0001 => it is stated as 100K per vega, which means 100k per 1% of Volatility move => Therefore, the variance must be 2,500 per variance. So, the variance notional must be 25M by multiplied by 10,000 You see it? Oh sorry i dont… I’ve been hung up on this for too long. I’ll either revisit or accept as it is. Thanks again for the help!! I rest my case for now. It’s okay buddy. It will come eventually. Pls take time to digest it. Just move on first and come back later. P.S. Don’t lose hope. Probably @S2000magician will come and help. 1 Like Thanksss! I’ll try to stay hopeful and stay alive! : D 1 Like I’ll try my best to clarify here: Volatility Scaling Factor: => To convert 1 percent to bps : 100 x 1% = 100 bps. (You cannot change the 1 percent to decimal point, otherwise 1% will not equal to 100 bps). Therefore, the scaling factor is 100 The notional is specified in volatility terms which is$100,000 per vega

\frac{$10,000,000}{100_{bps}} = \frac{$100,000}{1_{bps}}

This means if realized volatility is 1 bps ($100K per vega or volatility point) above the strike at maturity, the payoff will be equal to the Vega notional. (Just look at$10M divided by 100bps to find 1bps, which is $100,000) Next moving on to Variance Variance Scaling Factor: => As you know the variance is \sigma^2. Therefore, you can set the equation above from the volatility scaling factor {(100)^2}\times{1\%^2} = {10,000}\times{0.01\%} Therefore, the scaling factor for the Variance is 10,000. You might ask why this time 1% is converted to the decimal point first, I will show you why: Let’s say Var = 4% and if you were to convert 4% to Volatility in percentage without changing it to the decimal point first, you will get the wrong Vol. in percentage. Why? \sqrt{4\%} = 2\%. Because of that you have to convert from 4% to 0.04 first then sqrt it and multiply by 100. The ans will be 20% of volatility. Back to the Variance point, \frac{$25,000,000}{10,000_{bps}} = \frac{$2,500}{1_{bps}} You see if realized var is 1 bps ($2,500 per var or var point) above the strike at maturity, the payoff will be equal to the Variance notional. Actually, \sqrt{4\%}=20\%.

Your next line is correct, but let’s be careful.

1 Like

Thank you Sir. I was just trying to show @Stardust99 that without converting to the decimal point first and then sqrt the whole 4%, the result will be wrong.

Anyway, thank you again for reminding me Sir.  I don’t think i’m following your logic…but i do really appreciate your efforts! Thanks and stay well!

That’s okay. Don’t worry about it too much. Take times and come back when you can. It won’t go away. 