Firm's Equity Beta

[sklyte]

Anyone could help me explain why increase of allocation to equity says 50% to 75% will increase firm’s equity beta?
I know the plan asset beta will increase from 0.50 to 0.75, but could someone tell me how firm’s equity beta increase from 2 to 2.50? How to calculate ?This was shown in Schweser reading LOS 17.c

 

[Going_for_CFA_a]

I don’t have schweser so can’t look it up, but think about it like this:
On the asset side you have the pension portfolio. On the liability side you have the pension obligations. The difference between the two is the funded status and represents the claim of the firm’s equity holders on the pension portfolio (i.e. they get whatever is left once all plan participants’ obligations have been satisfied).
If you increase the pension portfolio’s allocation to equities, it’s beta should increase … since there are more equities (more exposure to the equity market). Likewise, the claim on the pension fund’s assets net of obligations (or the funded status) is now more sensitive to equities which is why the firm’s equity beta increases - the shareholders in the company, who have a claim on the pension fund’s residuals, are more exposed to the equity market because the pension fund allocated more to stocks.
Reading 17 was mainly conceptual, and the numbers were used to illustrate points … so I don’t know why Schweser is putting an emphasis on calculations. If you understand what I wrote, you’re good to go.

 

[sklyte]

Ok, thanks, In CFA Text Page 490 Table 4 also shows when equity allocation increase from 60 to 75%, the firm equity beta increase from 2 to 2.34, I guess the calculation is not emphasized here

 

[g3r41d]

Good point.
Pension plans are typically managed through ALM framework. Thus if there is over allocation to equities, your pension funded status will be extremely volatile due to the asset/liability mismatches. This increases the risk of the firm and thus increases the risk to equity holders which increases equity beta.

 

[calcfa2011]

This section is tough and I have spent alot of time going over it without fully grasping it. The calculation of Total Asset beta is derived from the right hand side. Then the Operating Asset beta is calculated from the Pension and Total Asset beta. Then it says that when the Pension Asset beta changes, it changes the Total Asset beta making it more risky. But the Total Asset beta is calculated from the Equity side. So which is it? Does the Equity beta drive the Total Asset beta or does the Total Asset beta drive the Equity beta?

 

[g3r41d]

calcfa2011 wrote:
This section is tough and I have spent alot of time going over it without fully grasping it. The calculation of Total Asset beta is derived from the right hand side. Then the Operating Asset beta is calculated from the Pension and Total Asset beta. Then it says that when the Pension Asset beta changes, it changes the Total Asset beta making it more risky. But the Total Asset beta is calculated from the Equity side. So which is it? Does the Equity beta drive the Total Asset beta or does the Total Asset beta drive the Equity beta?

Just treat it as when the pension asset beta changes, equity beta will also change (not dependent on any equation that is covered).

 

[Going_for_CFA_a]

calcfa2011 wrote:
This section is tough and I have spent alot of time going over it without fully grasping it. The calculation of Total Asset beta is derived from the right hand side. Then the Operating Asset beta is calculated from the Pension and Total Asset beta. Then it says that when the Pension Asset beta changes, it changes the Total Asset beta making it more risky. But the Total Asset beta is calculated from the Equity side. So which is it? Does the Equity beta drive the Total Asset beta or does the Total Asset beta drive the Equity beta?

You do sound confused.
Beta of the Operating Assets decreases by bringing the pension plan onto the balance sheet. This is because risk is correctly allocated under the economic balance sheet, whereas the standard balance sheet allocates 100% of the risk to the operating assets. From a corporate finance perspective, you are pricing the pension fund’s risk into cashflows from an independent project - doesn’t make sense.
The opertating asset beta should be unaffected by the equity allocation in the pensions fund. The total operating asset beta is affected because it includes both the operating assets and pension assets.
Total Equity beta is the sensitivity of the shareholders’ claim on the residuals of all projects undertaken by the firm. This includes the NPV of operating projects + the funded status of the pension plan. So the more you mismatch the risks between pension plan assets and liabilities (i.e. you have fixed rate obligations being financed by a higher degree of equity returns), the more sensitive is the claim on the funded status to the equity market -> the higher the beta of the firm’s equity capital.