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# P2 Focus review problem

#### Kavita.bhangdia

##### Active Member
Hi David,
In P2 Focus review problem (5th of 8: operational risk), you have divided the spread 0.16 by the cost of security 72.

Why is that..

I had just multiplied 72000*.5*.16 for Liquidity cost which is different from your 72000*.5*.16/72 liquidity cost

Thanks,
Kavita

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Kavita.bhangdia

I think you want 1,000 shares * 0.5 * $0.16 =$80.00 for the liquidity cost, if you want to do it that way, which is fine?
To use 0.16/$72.00 is simply to derive liquidity cost in terms of percentage. Either way, the LC here is$80.00 or 0.111% = 0.16/72 * 0.5.

See the source (which is a GARP FRM practice exam question at https://www.bionicturtle.com/forum/threads/l2-1-13-liquidity-risk-operational.4166/ i.e.,
Question: You are a manager of a renowned hedge fund and are analyzing a 1,000 share position in an undervalued but illiquid stock BNA, which has a current stock price of USD 72 (expressed as the midpoint of the current bid-ask spread). Daily return for BNA has an estimated volatility of 1.24%. The average bid-ask spread is USD 0.16. Assuming returns of BNA are normally distributed, what is the estimated liquidity adjusted daily 95% VaR, using the constant spread approach?

a. USD 1,389
b. USD 1,469
c. USD 1,549
d. USD 1,629

Explanation:
Daily 95% VaR = 72,000 * (1.645 * 0.0124) = USD 1469
Liquidity cost = 72,000 * (0.5 * 0.16/72) = 80
LVaR = VaR + LC = 1549

Topic: Operational and Integrated Risk Management
Subtopic: Liquidity risk
AIMS: Describe and calculate LVaR using the Constant Spread approach and the Exogenous Spread approach.
Reference: Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005), Chapter 14.

#### Kavita.bhangdia

##### Active Member
Hi David,
What I understand is that you have computer the liquidity cost for 1000 shares.. (72000*.5*.16/72)
But I was calculating liquidity cost for the entire position value AND NOT for 1000 UNITS OF SHARE = 72000*.5*.16.

I think the liquidity cost should be on units of share..
so it should be just 0.5*.16*1000.

AM I right?

Thanks
Kavita

#### Deepak Chitnis

##### Active Member
Subscriber
Hi @Kavita.bhangdia, I think you are something missing here. Liquidity cost should be=72000*(0.5*0.16/72)=79.99 or 80. Because as per the formula liquidity cost=P*(0.5*spread). Hope that helps!
Thank you

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
I do think the units in liquidity cost can be confusing, they give people trouble every year, as far as I can tell. In this question, we are given that "The average bid-ask spread is USD 0.16" which is per share. I think we can look at this at least three ways, but it all cases, the key relationship is the assumption that liquidity cost (LC) is one-half the bid-ask spread (under the simplest and most testable approach which Dowd calls the "constant spread approach" and which is betrayed by the fact that volatility of the spread is not provided as an assumption):
• Like GARP's answer, we can retrieve the LC of the position, which is 0.5* $0.16 per share * 1,000 shares =$80.00; i.e., LC of the position.
• We can compute LVaR(%) = VaR(%) + LC(%), where LC(%) = 0.16/72 = 0.222% such that LVaR(%) = (1.24%*1.645)+0.222% = 2.1507% and LVaR($) = 2.1507%*(1,000 *$72.00) = $1,549 • We can compute$LC per share = 0.50 * $0.16 =$0.08, and add that to the per share VaR of $1.468 =$72.00*1.24%*1.645, so the per share LVaR = $1.468+0.08 =$1.549.
I think it's all the same except to the extent we are asked for either:
• LC of the position
• LC as a percentage, which is likely an input, or
• LC per share.
Mathematically, it is interesting to me in the sense that LC, in a way, is just "increasing the volatility." In this case, daily vol 1.24%, and VaR just multiplies that by a deviate (1.645) to get 2.04%. Then LC just "expands" that to 2.1507%. I hope that helps!