# Var quiz

A good example problem I came upon in EOC. \$100M portfolio 50% US Bonds, 50% UK Bonds US Bonds: Monthly Return = .85% Standard Deviation = 3.2% UK Bonds: Monthly Return = .95% Standard Deviation = 5.26% Correlation between the 2 = .35 Using analytical method, calculate: 5 percent monthly VAR 5 percent weekly VAR

Monthly Portfolio SD: sqrt[(.5^2*3.2^2)+(.5^2*5.26^2)+(2*.5*.5*.35*5.26*3.2)] = sqrt[40.8532] = 6.391651 Portfolio ER: (.5*.85)+(.5*.95) = .425 + .475 = .9 Monthly VAR: .9 - [1.65*6.391651) = .9 - 10.54622 = (-9.6422)/100*100000000 = -9646223.8 Weekly ER: (.9*12) / 52 = .207692 Weekly SD: (6.391651*sqrt(12)) / sqrt(52) = 22.14133 / sqrt(52) = 3.0745 Weekly VAR: .207692 - (1.65*3.0745) = (-4.85855)/100*100000000 = -4858549.7

The answers are: Monthly Var: \$4.91M (4,916,250) Weekly Var: \$2.58M (~ 2,585,000) Check your SD calc above, formula is correct but result is wrong. Besides that I think it looks good.

Should be: Monthly Portfolio SD: sqrt[(.5^2*3.2^2)+(.5^2*5.26^2)+(2*.5*.5*.35*5.26*3.2)] = sqrt[40.8532] = 3.524557 Monthly VAR: .9-[1.65*3.524557] = -4.91552/100*100000000 = -4915519 Weekly SD = 3.524557*(sqrt(12/sqrt(52)) = 1.693142 Weekly VAR = .207692-[1.65*1.693142] = -2.58676/100*100000000 = -2586765

I also get -4,915,518.57 as Monthly Var and -2,585,992.45 as weekly Var But I like bpdu’s presentation which is apt for essay question

They could have added one more bit of complexity to the problem by adding - the UK bond returns and risk measures are in “local currency”. - and they give you the correlation between the UK asset returns with the exchange rate (0.3) and return on the US/UK exchange rate (-1.5%) nice practice example, thx

yodhava Wrote: ------------------------------------------------------- > They could have added one more bit of complexity > to the problem by adding > > - the UK bond returns and risk measures are in > “local currency”. > - and they give you the correlation between the UK > asset returns with the exchange rate (0.3) and > return on the US/UK exchange rate (-1.5%) > > nice practice example, thx It would be the standard deviation of exchange rates, not the return correct?

Paraguay Wrote: ------------------------------------------------------- > yodhava Wrote: > -------------------------------------------------- > ----- > > They could have added one more bit of > complexity > > to the problem by adding > > > > - the UK bond returns and risk measures are in > > “local currency”. > > - and they give you the correlation between the > UK > > asset returns with the exchange rate (0.3) and > > return on the US/UK exchange rate (-1.5%) > > > > nice practice example, thx > > > It would be the standard deviation of exchange > rates, not the return correct? Yeah Paraguay, they would also need to give you the standard deviation of exchange rate return over that period. But you also need the exchange rate return so that you can calc the UK bonds return in US currency. UK Bond Return (in usd) = UK Bond return (local) + s ( USD/UK return) UK Bond Risk (in usd) = SQRT ( UK Bond local ^2 + s^2 + 2*UK-L*s*Corr(UK-L,s) ) Right?

yodhava Wrote: ------------------------------------------------------- > Paraguay Wrote: > -------------------------------------------------- > ----- > > yodhava Wrote: > > > -------------------------------------------------- > > > ----- > > > They could have added one more bit of > > complexity > > > to the problem by adding > > > > > > - the UK bond returns and risk measures are > in > > > “local currency”. > > > - and they give you the correlation between > the > > UK > > > asset returns with the exchange rate (0.3) > and > > > return on the US/UK exchange rate (-1.5%) > > > > > > nice practice example, thx > > > > > > It would be the standard deviation of exchange > > rates, not the return correct? > > Yeah Paraguay, they would also need to give you > the standard deviation of exchange rate return > over that period. > But you also need the exchange rate return so that > you can calc the UK bonds return in US currency. > > UK Bond Return (in usd) = UK Bond return (local) > + s ( USD/UK return) > > UK Bond Risk (in usd) = SQRT ( UK Bond local ^2 > + s^2 + 2*UK-L*s*Corr(UK-L,s) ) > > Right? Yeah you would need all of them. This test is not passable.

Come on Paraguay, of all the folks in this board, you probably would be in the Top 10% band who passed… if CFA were to ever give such stats. relax. examples like this with so much mechanical calc is not CFA’s modus operandi That’s why we got a computer…AF isn’t hosted on 12C.