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Return and Variance 7
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Lecture1.1
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Lecture1.2
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Lecture1.3
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Lecture1.4
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Lecture1.5
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Lecture1.6
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Lecture1.7
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Solving Equations 5
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Lecture2.1
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Lecture2.2
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Lecture2.3
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Lecture2.4
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Lecture2.5
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Capital Allocation Line 6
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Lecture3.1
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Lecture3.2
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Lecture3.3
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Lecture3.4
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Lecture3.5
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Lecture3.6
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Diversification 3
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Lecture4.1
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Lecture4.2
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Lecture4.3
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Investment Sets 3
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Lecture5.1
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Lecture5.2
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Lecture5.3
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Portfolios 7
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Lecture6.1
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Lecture6.2
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Lecture6.3
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Lecture6.4
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Lecture6.5
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Lecture6.6
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Lecture6.7
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Capital and Security Market Lines 3
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Lecture7.1
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Lecture7.2
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Lecture7.3
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Arbitrage 3
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Lecture8.1
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Lecture8.2
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Lecture8.3
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Dividend Discount Model 2
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Lecture9.1
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Lecture9.2
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Fixed Income 4
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Lecture10.1
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Lecture10.2
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Lecture10.3
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Lecture10.4
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Duration and Immunization 4
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Lecture11.1
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Lecture11.2
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Lecture11.3
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Lecture11.4
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Immunization
As we saw, there is interest rate risk for bonds that we can measure with duration. The way to eliminate this risk is to get a portfolio where the total duration is equal to 0.
Let’s say we still have that bond with face value of 1000 from before, and we also have a bond with a price of 900 and duration of 6. What amount would we need to short to make our total portfolio have a duration of 0?
1*p1*d1-x*p2*d2 = 0 for this to happen, so let’s run the numbers to solve for x.
print((p1*d)/(900*6))
print((p1*d)/(6))
So if we allocate 0.4875188402851868 as much, or 438.76695625666815 we will hedge interest rate risk.
This is not perfect though, you would need to rebalance after changes, duration isn’t exact.
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