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Jorion, Chapter 7 - Portfolio Risk: Analytical Methods


Hi David

In the notes of Jorion, Chapter 7 - Portfolio Risk: Analytical Methods we are given a table with the risk and return - optimising positions where we are given the Final position weight w(i). Are we expected to be able to calculate this in the exam? and if so, how is it calculated? Many thanks.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @kik92 I think you are referring to the two optimization problems at the end of Jorion (my exhibits rebuild his, but with color! They each have a sheet in our learning XLS at https://www.bionicturtle.com/topic/learning-spreadsheet-jorion-chapter-17/ where one is "Ch7.5.1-Risk-Min" and the other is "Ch7.5.2-PM"). Because the solutions are iterative, I cannot imagine GARP asking for the calculation; however, we do know from feedback that GARP has asked about this conceptually, which is consistent with the LOs:
• Apply the concept of marginal VaR to guide decisions about portfolio VaR.
• Explain the risk-minimizing position and the risk and return-optimizing position of a portfolio.
• Explain the difference between risk management and portfolio management, and describe how to use marginal VaR in portfolio management.

GARP does like to query the retrieval of the portfolio VaR metrics (e.g., marginal VaR, component VaR, incremental VaR) as you can see in virtually every practice paper they have published (and I have iterated feedback with them on this overall topic extensively).

The easiest way to query this conceptually (without requiring a calculation) is to identify which direction to re-allocate the portfolio; for example, if the goal is to reduce risk (or instead, to increase the Sharpe ratio), how can we decide that based on marginal VaR (or beta)?.

I just yesterday posted some help for @meenalbaheti on this topic at https://www.bionicturtle.com/forum/threads/p2-t8-3-portfolio-value-at-risk-var-methods-jorion.4794/ My recommendation is not to sweat solving the numbers but rather just understand how either goal (that is, are we seeking the least risk or the highest return-per-risk?) informs a decision to re-allocate, as below. I hope that helps!
Hi @meenalbaheti These are difficult ideas to convey exclusively in words without referencing the math/XLS; if you are truly interested, I would recommend looking at the learning XLS to which I have referenced. But briefly:
  • Minimum risk (aka, global minimum risk) is the green arrow below (this is Jorion's Figure 7-5, which is the assignment for these concepts), it is the portfolio with the lowest standard deviation (i.e., risk only). The blue arrow points to the optimal portfolio which has the highest Sharpe ratio (i.e., excess return per unit of risk). The optimal portfolio will have higher risk and return.
  • Re: "If we shift from low sharpe ratio to higher Ines than we are reducing the risk," the Sharpe ratio (or the excess return per beta) is a ratio of excess return per unit of risk, so improving the Sharpe ratio is not necessarily reducing risk, if the increase in return offsets (per the diagram below: shifting form the minimum risk portfolio to the optimal [highest Sharpe] generally implies an increase in risk
  • If the goal is to reduce risk (per question 3.4) then we want to increase the allocation to the less risky position (i.e., lower marginal VaR)
Here is Jorion's example (which I replicated in my XLS):
  • Original position
    • $2.0 mm CAD + $1.0 mm EUR = $3.0 mm portfolio
    • CAD: ΔVaR(CAD) = 0.0527 and E[R(CAD)]/β(CAD,P) = 5.0%/0.6148 = 0.1301
    • EUR: ΔVaR(EUR) = 0.1516 and E[R(EUR)]/β(EUR,P) = 8.0%/1.7705 = 0.0282
  • To minimize risk, we increase allocation to position with lower ΔVaR which is the CAD, such that global minimum is found at:
    • CAD --> 85.21% and EUR --> 14.79%, where
    • Both will have betas equal to 1.0 and identical ΔVaR = 0.0759 (see how CAD's marginal VaR increased and EUR's marginal VaR decreased?)
  • To maximize Sharpe (optimal return per risk) we increase allocation to position with higher E[R(EUR)]/β(EUR,P) which is also the CAD, where optimal is founds at:
    • CAD --> 90.21% and EUR --> 9.79% where
    • Both will have identical E[R(.)]/β = 0.077 (see how CAD's decreased from 0.1301 to 0.077 and EUR's increased from 0.0282 to 0.077?). Phew, I hope that's helpful!