<p>This video by explains the concept of mapping fixed income portfolios to risk factors.</p>



<p>Why map portfolios to risk factors? It's a shortcut because portfolios are complicated; e.g., even delta-normal VaR employing a covariance matrix contains n(n+1)/2 pair-wise correlations in a dreaded "curse of dimensionality." The reality of a portfolio's true risk exposure is both ultimately unknowable and undeniably complex. Mapping reduces the portfolio to a few key characteristics. The approximation sacrifices accuracy but makes the portfolio amenable to, say, stress testing.</p>



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https://www.youtube.com/watch?v=CYQ2_Xzr8uk
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<p><em>This video is developed by David from Bionic Turtle.</em></p>

Mapping a Fixed Income Portfolio to Risk Factors

<p>Bond risk can be measured by "price returns value at risk (VaR)" where the price returns VaR is linked to yield VaR with duration.</p>



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https://www.youtube.com/watch?v=WUHC-nb-7Hg
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<p><em>This video is regarded by David from Bionic Turtle.</em></p>

Bond Returns Value at Risk (VaR) as Bond Risk

<p>A European stock option can be mapped to two positions: 1. A Long position in the asset, plus 2. a short position in underlying bill (i.e., interest rate factor).</p>



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https://www.youtube.com/watch?v=3wEBJbUuKfQ
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<p><em>This video is developed by David from Bionic Turtle.</em></p>

Mapping a European Stock Option

<p>First, we used the formula for the value of a forward contract to identify the three risk factors. This is the essential mapping idea: we characterize the portfolio as a set of exposures to underlying risk factors. In this case, a forward currency contract maps to a long position in a foreign currency spot rate, a long position in a foreign interest rate (EUR bill) and a short position in a domestic interest rate (USD bill).</p>



<p>Second, we develop input assumptions: VaR for the risk factors and the correlation matrix. Third, we use the formula for portfolio VaR: post-multiply R(xV) and then pre-multiply (xV)'R(xV).</p>



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https://www.youtube.com/watch?v=Um8e_teI_dw
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<p><em>This video is developed by David from Bionic Turtle.</em></p>

VaR of Forward Foreign Currency Contract

<p>This video illustrates the calculation of undiversified value at risk (VaR) for a two-bond portfolio.</p>



<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
https://www.youtube.com/watch?v=SqZaAl5g_8U
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<p><em>This video is developed by David from Bionic Turtle.</em></p>

Undiversified Bond Value at Risk (VaR)

<p>In the previous video, we learned about the calculation of the <a title="Undiversified Bond Value at Risk (VaR)" href="https://financetrain.com/undiversified-bond-value-at-risk-var/">un-diversified VaR of the two-asset bond portfolio</a>. This video explains <a href="https://geni.us/OAPM">Jorion's</a> Table 11-4 which calculates diversified value at risk (VaR) for the same bond portfolio. The key difference is that diversified VaR should be lower to reflect the benefit of imperfect correlations.</p>



<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
https://www.youtube.com/watch?v=cjguDOUswDA
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<p><em>This video is developed by David from Bionic Turtle.</em></p>

Diversified Bond Value at Risk (VaR)

VaR Mapping

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VaR Mapping

Lessons

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