Pension asset's effect on WACC

Schweser Vol II Question 9 Address the potential effect on SHCA of investing 100% of the plan’s assets in equity securities on SCHA’s WACC, and to the firm’s capital structure, assuming management wants to maintain the firm’s current overall level of risk I understand the logic of the answer. The greater the exposure to equities in the SHCA pension plan, the higher the company’s overall risk profile and its WACC. To keep the equity risk the same, management has to deleverage. What I do not understand is how this whole process is translated to the asset liability balance sheet below: How does the beta change for each item? Assets Beta Liabilities and Equity Operating assets 500 0.48 Firm liabilities 200 Pension assets 100 0.6 Pension liabilities 100 Total 600 0.5 Equity 300 Total 600 my thought: by increasing equity investment, beta 0.6 increase => overall total beta on asset 0.5 increase How about On the liability side ???

You just need to know the logic, the math is not given or shown. I don’t understand it either and read the article a few times. It says in a few places to just take their word for it and not get bogged down with the math. I went through the math and all things being equal, when you increase equity to 100%, there is no indication on how to change the liability side, if it stays the same, then asset beta actually goes down. It’s a bit contradictory because based on the math they do show, there is even a bigger WACC mis-pricing.