Total Asset Beta

***Given the equations below, schweser says that if you include Pension Assets & Liabilities in the firm’s balance sheet, it will reduce the Total Asset Beta. Can someone explain why? In relation to the equations below, it would seem that if you add pension assets to the first equation, it would increase the Asset Beta. I’m not sure what the effect would be when adding the pension liabilities.

I use the following formulas to determine Total Asset Beta:

  1. (Operating Assets * Operating Asset Beta) + (Pension Assets * Pension Asset Beta) = Total Asset * Total Asset Beta

  2. (Operating Assets * Operating Asset Beta) + (Pension Assets * Pension Asset Beta) = Equity MV * Equity B

your equation number 2) should be

operating asset / TOTAL asset*Operating Asset Beta + Pension Assets/TOTAL asset * Pension Asset Beta = Equity MV / (equity + liability) * Bequity

Since liability will be larger ( by adding the liability of the pension plan ) the rightside of you equation will be lower. liability of a pension plan has 0 beta, that why you dont add liability/ (equity + liability) * B liability

since Equity MV / (equity + liability) * Bequity MUST be lower than before,TOTAL asset beta should be lower also.

Could someone post an example with some actual numbers? This concept is still not clear to me. Appreciate it!

I always start drawing up a table:

ASSETS: Value Beta LIABILITIES: Value Beta

Oper Assets 80 1.5 Debt 20 0

Equity 60 2

Total Assets 80 1.5 Total D+E 80 1.5

Total Asset beta was calculated as follows: 20/80 * 0 + 60/80 * 2 = 1.5

Now let’s assume that they have a Pension fund (fully funded).

ASSETS: Value Beta LIABILITIES: Value Beta

Oper Assets 80 1.35 Debt 20 0

Pension Assets 20 0.60 Pension Liab 20 0

Equity 60 2

Total Assets 100 1.2 Total D+E 100 1.2

Total Asset beta is now = 20/100 * 0 + 20/100 *0 + 60/100 * 2 = 1.2

And if we assume that Pension funds beta is 0.6, then

Operating Asset Beta would be = (1.2 - 20/100 * 0.6)/(80/100) = 1.35

Hope this didn’t make you confused even more :slight_smile:

Adding pension assets and pension liabilities will result in: - RHS equity weight to decrease due to inclusion of pension liabilities - LHS total asset beta to decrease (due to earlier reduce in equity weight) - LHS operating asset beta to decrease (since now instead of just operating asset you are including pension asset as well. This is also compounded by the earlier reduction of total asset beta) - WACC to decrease.

The important point is that if you include pension liabilities in the capital structure, there is a greater percentage of liabilities than before (in the example from kurmanal, the % goes from 25% to 40%. And since the liabilities have a beta of zero, this will push the total asset beta down.

The example combined with movingonup’s blurb clarified it for me. Thanks a bunch!!!