Notional Portfolios - Chapter 24

[Blits]

Hi

I am having trouble with the concept of Notional Portfolios as discussed in chapter 24 of the notes.

Example on page 16 of the notes - I do not understand how they arrive at the initial formula for Assessed Value. I do understand the derivation proving that D/d is equivalent to DVequity/MVequity but I do not understand why multiplying the Market Value of the entire portfilio by DVequity/MVequity (similarly for bonds)?
Further I do not understand the answer and the explanation of Question 24.9.
Question 24.12 - Equity Portion I assume the formula used is (% of notional portfolio in equities)x(D/d). I think D should be 4%? Gilt Portion - as per the notes the value of an undated bond, with Coupon C is C/i. I think C is 2.5 and i is 10%?
Thanks very much for your help

 

[Mark Willder]

Example on page 16 of the notes - I do not understand how they arrive at the initial formula for Assessed Value. I do understand the derivation proving that D/d is equivalent to DVequity/MVequity but I do not understand why multiplying the Market Value of the entire portfilio by DVequity/MVequity (similarly for bonds)?

Notional portfolios use a discounted cashflow approach to valuing the assets. We know the market value of the assets in equities (and bonds), but we need to convert this value into a discounted value. Therefore we use the factor DVequity/MVequity which tells us the discounted value of 1 pound of equity.

Further I do not understand the answer and the explanation of Question 24.9.

This question says that a rise in the market value has probably no effect on the notional portfolio value.

The reason is linked to my explanation above. Notional portfolios use a discounted cashflow approach to valuing the assets. Therefore this value will only change if we change our assumptions about future cashflows or the discount rate. These assumptions are often kept fixed for long periods of time. We probably wouldn't change our assumptions just because market values had moved.

This is an advantage, because it leads to stable assets values. It is also a disadvantage, as it means that notional portfolio values are not realistic ie they may be very different to market values.

Question 24.12 - Equity Portion I assume the formula used is (% of notional portfolio in equities)x(D/d). I think D should be 4%? Gilt Portion - as per the notes the value of an undated bond, with Coupon C is C/i. I think C is 2.5 and i is 10%?

Yes. we are using D/d for equities (equivalently D/(i-g)).

D gives us the cashflows which are based on actual market data, so D is 5%.

We discount these at the assumed rate of interest i-g = 9.5 - 5.5 = 4% = d.

For the bond we use DVbond/MVbond.

MVbond is given by C/i with i at the market rate of 10%.

DVbond is given by C/i with i at the assumed interest rate of 9.5%.

So DVbond/MVbond = (C/9.5%)/(C/10%) = 10/9.5 (note the value of C is irrelevant as it cancels)

Best wishes

Mark