Var quiz problem, percent, monthly, example, between

AnalystForum

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

bodhisattva

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.

Valores

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

NO EXCUSES

liangfeng

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

lcai

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?

ohai

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?

cityboy

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.

mp3bu

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

Windjammer

That's why we got a computer...AF isn't hosted on 12C.