FRM Learning Objective: Define, calculate, and distinguish between the following portfolio VaR measures: diversified and undiversified portfolio VaR, individual VaR, incremental VaR, marginal VaR, and component VaR.
super helpful! If i have a portfolio with many different assets (including derivatives, swaps, bonds, equities, commodities) etc. and I am able to calculate the portfolio VaR as well as marginal VaR per risk type (eq/commodities/int rate/credit/volatilites), how can i get each risk type's component VaR? how can i scale the marginal VaR in this instance.
Thanks for the video! A question. For Stock A (negative position) shouldn't the Component VaR be negative? Should portfolio VaR decrease? Example, if my portfolio is 8000+2000 and VaR is -10%, if I have 8,000 and -2000 VaR should be lower than 10%, correct? So for example VaRa = -12% and VaRb = +2%... -12+2 = -10% Can you help me?
Hello Giulio. The component VaR of stock A is positive because both its weight and beta are negative. Therefore, Component VaR of A = PortfolioVaR(%) * Weight A * Beta A is positive. Another way to explain this is by interpreting component VaR as risk contribution. The component VaR of stock A measures how much its position contributes to the portfolio risk. Since the returns of the two stocks are negatively correlated, including a long position in stock A (of say +5000) to a portfolio containing stock B would have reduced the portfolio risk. But a short position in stock A does the opposite: it increases the portfolio risk. Hence, the component VaR of stock A is positive.
@@finRGB ok perfect, so if beta had been positive (with negative weight), then the component var would have been negative. it is clear thank you very much
Hello Luis. When stock A has an exposure of -20,000 the total value of portfolio will be zero. In that case, the individual VaR for stock A position will be 1914 (four times the value given in the question, since position is four times as much) and VaR for overall portfolio can be calculated using the formula given below: sqrt(VaRA^2 + VaRB^2 + 2*sign(x1)*sign(x2)*VaRA*VaRB*Corr12) which you can check comes out to 1993.2.
I tried to replicate this example and calculated delta VaR of the portfolio and get 90,95 as you. However, when calculating the marginal VaRi you would get 90,95/(-1000) = -0,091 and 90,95/1000 = 0,091. Using this, my cvar1 is 454,75 and cvar2 is 1819. They do not sum up to the VaR of the portfolio. Where is my mistake?
Your mistake is that the 90.95 (change in VaR) that you have used for calculating the MVaR occurs when BOTH stock positions have been altered. MVaR for any position should be calculated by shifting the exposure of that position by a tiny amount "keeping the exposure of all other positions unchanged".
@@finRGB Thank you. I have recalculated the example and get mvar1=-0.0785 and mvar2=0.0137. When calculating the contributions cvar1=392.393 and cvar2=273.188. When I add up the cvars I should come up to 650, but I get 665.58 instead. How can this be explained?
@@TheHawkingSolutionHD It seems your bump in exposure to calculate MVaR is not "tiny". The current portfolio vol is 2.6299% and hence, VaR is 650.9036. If you recalculate portfolio VaR for exposures -4999 and 20000 (i.e. exposure for stock A bumped up by $1 and for stock B unchanged), the new portfolio vol comes to 2.6294% and hence, VaR comes out to be 650.8274. The change in VaR is -0.07617 which is the MVaR for stock A in the video.
@@finRGB Thats it, I calculated the MVaR with the change of 1000. I got the solution using a tiny amount of change. Thanks you so much and for the great explanation!
FRM Learning Objective: Define, calculate, and distinguish between the following portfolio VaR measures: diversified and undiversified portfolio VaR, individual VaR, incremental VaR, marginal VaR, and component VaR.
Very Well explained
Great explanation
Super helpful example thanks
Really good video
Thank you for the appreciation, Alex.
super helpful! If i have a portfolio with many different assets (including derivatives, swaps, bonds, equities, commodities) etc. and I am able to calculate the portfolio VaR as well as marginal VaR per risk type (eq/commodities/int rate/credit/volatilites), how can i get each risk type's component VaR? how can i scale the marginal VaR in this instance.
I can understand how to calculate the beta value?
Thanks for the video! A question. For Stock A (negative position) shouldn't the Component VaR be negative? Should portfolio VaR decrease?
Example, if my portfolio is 8000+2000 and VaR is -10%, if I have 8,000 and -2000 VaR should be lower than 10%, correct? So for example VaRa = -12% and VaRb = +2%... -12+2 = -10%
Can you help me?
Hello Giulio. The component VaR of stock A is positive because both its weight and beta are negative. Therefore, Component VaR of A = PortfolioVaR(%) * Weight A * Beta A is positive.
Another way to explain this is by interpreting component VaR as risk contribution. The component VaR of stock A measures how much its position contributes to the portfolio risk. Since the returns of the two stocks are negatively correlated, including a long position in stock A (of say +5000) to a portfolio containing stock B would have reduced the portfolio risk. But a short position in stock A does the opposite: it increases the portfolio risk. Hence, the component VaR of stock A is positive.
@@finRGB ok perfect, so if beta had been positive (with negative weight), then the component var would have been negative. it is clear thank you very much
Nice video! What happens if the value of position in stock A is -20.000? By the formula, the VaR would be 0, but the stocks are not 100% correlated.
Hello Luis. When stock A has an exposure of -20,000 the total value of portfolio will be zero. In that case, the individual VaR for stock A position will be 1914 (four times the value given in the question, since position is four times as much) and VaR for overall portfolio can be calculated using the formula given below:
sqrt(VaRA^2 + VaRB^2 + 2*sign(x1)*sign(x2)*VaRA*VaRB*Corr12)
which you can check comes out to 1993.2.
I tried to replicate this example and calculated delta VaR of the portfolio and get 90,95 as you. However, when calculating the marginal VaRi you would get 90,95/(-1000) = -0,091 and 90,95/1000 = 0,091. Using this, my cvar1 is 454,75 and cvar2 is 1819. They do not sum up to the VaR of the portfolio. Where is my mistake?
Your mistake is that the 90.95 (change in VaR) that you have used for calculating the MVaR occurs when BOTH stock positions have been altered. MVaR for any position should be calculated by shifting the exposure of that position by a tiny amount "keeping the exposure of all other positions unchanged".
@@finRGB Thank you. I have recalculated the example and get mvar1=-0.0785 and mvar2=0.0137. When calculating the contributions cvar1=392.393 and cvar2=273.188. When I add up the cvars I should come up to 650, but I get 665.58 instead. How can this be explained?
@@TheHawkingSolutionHD It seems your bump in exposure to calculate MVaR is not "tiny". The current portfolio vol is 2.6299% and hence, VaR is 650.9036. If you recalculate portfolio VaR for exposures -4999 and 20000 (i.e. exposure for stock A bumped up by $1 and for stock B unchanged), the new portfolio vol comes to 2.6294% and hence, VaR comes out to be 650.8274. The change in VaR is -0.07617 which is the MVaR for stock A in the video.
@@finRGB Thats it, I calculated the MVaR with the change of 1000. I got the solution using a tiny amount of change. Thanks you so much and for the great explanation!