# operating asset beta

Ok, just getting to the end of SS# 5 and I can’t for the life of me figure this out. First real point of frustration so far so I guess thats good. When you calculate operating asset beta before pension assets, why would it change later? I understand total asset beta will change because you are bringing in the pension assets, but I don’t understand how operating assets change when their value doesn’t change. To me it seems that the only thing that should change is their weighting in calculating total asset beta. Any help with this?

traditional balance sheet - use Debt (with a beta of 0), Equities with the Equity Beta and calculates the Asset Beta (Assets are only the Operating Assets). Equity Beta * Equity MV / (Total Assets (excl. pension asset)) = Asset Beta Since the assets only have operating assets - asset beta = operating asset beta. With the Economic Balance sheet: (assuming Pension Assets = Pension Liabs – fully funded pension plan). when you introduce the pension assets - total assets increase, and total balance sheet beta changes since Equity beta * Equity MV / (Total Assets incl. Pension Assets) = Total Asset beta. Operating Asset * Op Asset beta + Pension assets * Pension assets beta = Total Assets * Total Asset beta. As a result of introduction of the pension asset beta and as a result of the above equality - operating assets beta changes.

Very much appreciate the explanation CP. You don’t have to continue with this, but I’m still stuck on this point. The beta of the operating assets doesn’t seem like it should change as long as pension assets are broken out (which they are in most examples). This would lead me to conclude that the operating assets (not total assets) haven’t changed, and therefore why should their beta. I understand the formulas above, it just seems like in your last one formula, the op asset beta shouldn’t change from when you calc’d it before adding pension assets. Pension assets is separate when computing total asset beta. I agree that the total asset beta changes, but I think it should be because of the weight. You aren’t actually adding anything different to op assets other than their effect on total asset beta. Those same assets’ beta doesn’t magically change. Its effect does though. Does that even make sense?

I think this can seem to be confusing because we were taught in level 2 that the risk level of assets are not affected by the capital structure (i.e. the asset beta remains the same no matter how much debt is used in the capital structure). The point of this exercise is that we can calculate the beta of total assets. First, we find the beta of total assets with pension assets and liabilities included. Because we know the beta of the total assets and the beta of the pension assets, we can then back into the implied beta of the operating assets. This formula directly relates to the risk budget. Point being that a firm can assume more risk in its core business depending upon the how the pension portfolio is constructed. This would implie more risk in operating assets, but the same overall level of risk for the firm. This did not click for me at first, but then I had an “ah ha” moment. Just have to step back and think of the big picture here.

pension assets are not included at all. so based on that aspect - the operating assets that were calculated would by nature have a higher beta. Additionally what Mr. Merton is trying to say is - all of this risk (beta) is being assigned to the operating assets - hence to the WACC. when pension assets (which are part equity and part fixed income) is included - the total beta of the firm’s assets reduces (since the equity beta is spread out over a larger base (now including pension liabs)). pension assets beta is known. total asset beta now gets apportioned between the pension and op assets - so op assets beta will change. weight is one aspect of it all. but the other bigger part is a new component being included in the calculations (which affects the weight as well). since the total asset beta changed, the operating asset beta will also change. it is not a weight thingie alone. (take it for what its worth).

I’ll let this one be. Thanks for the input fellas (assuming), my mental block is still somewhat hung up on the point WorldsGreatest made about betas not changing despite capital structure. I see what both of you are saying and it makes sense that equity beta is spread over a larger asset base with pensions included. I don’t like the fact that “pension asset beta is known.” Just a minute ago before we added pension assets, operating asset beta was known. Now suddenly we are recalculating it. ARGH!!! I can follow the steps and even see the big picture of why it makes sense that WACC goes down. But this little step in the calculations is just not getting me to “ah ha” land. Ah well, sometimes you have to muscle through without 100% understanding. Thanks for your time, now get back to studying. I already feel bad taking the amount of time I have! Best of luck.

this also relates to the fact that once the operating asset’s true risk level is known - in order to implement - either leverage would need to be reduced or increased depending upon how the firm wants to move (100% equity on Pension assets or 100% bonds on Fixed Assets). When 100% Equity is pushed on the Pension assets - they become more risky. In order to keep the Equity Beta of the firm the same as before - you would now need to reduce the total risk of the firm - which would only be possible by reducing Debt - so your leverage needs to go down. Risk Budget is what it is in the final analysis.

CP and WorldGreatst have given an elaborate explanation, which is already complete. I will just attempt to get you your ‘ah ha’ feeling. I got mine the next day after doing the reading As WorldGreatest said, Risk of Project is independent of Capital Structure it is funded with. The catch is, risk of Project may be independent of Capital Structure, but risk to Shareholder’s Equity is NOT. Risk to shareholder’s Equity comes from Risk of Project PLUS the risk added by Financial Leverage. Now, in this case, we can take that firm has 2 Projects: Project A: Operating Assets Project B: Pension Assets There are 2 things to understand here: 1. Shareholder’s Equity is UNCHANGED, whether we use Traditional B/S or the Modified B/S including Pension Assets and Pension Liabilities. 2. Market has already priced the stock based on Risks from both the Projects A and B. meaning, Equity Beta (Risk to Shareholder’s Equity), already includes risk of Project B as well. (Market is smart and it already looks beyond your traditional B/S) Next, Case 1: Traditional B/S We unlever Equity Beta to get Intrinsic Risk of Project A. Since, Equity Beta is already having risks from both Projects, if after unlevering, we put all that risk on Project A, it will be more than what the Project A actually has. Thus, in this case, Project A’s Beta is overestimated and hence its WACC is overestimated. Case 2: Modified B/S We unlever Equity Beta to get Risks from Both Projects. Then we weight it accordingly between Project A and Project B. In this case, we get true intrinsic Risk of Project A, which is lower than as calculated in Case 1. Hence, WACC for Project A is also lower. That is how and why Beta of Operating Assets (project A) changes. Hope this helps.

Here is how I learned to do it 1/ Write down two columns, one side has the assets, the other the liabilities. Both are the sums of both the operating assets and the Pension assets. 2/ In the Right hand side, calculate the beta of the Equity as a proportion of the total amount. Assuming that the debt is zero, this will be a smaller number than just the Operating asset beta. Say that this value is A 3/ On the left hand side, calculate the beta for the Pension assets, this value will be B 4/ Subtract A from B WHAT EVER IS LEFT OVER, that is the new operating beta which will be smaller than the original beta without Pension assets. I may have fudged some descriptions, but that is how I remember it and was able to get 6/6 on the practice problems

Thanks for the wonderful explanation. Here is my understanding and it helps me. 1, Total Asset beta*(Total Assets excl. Pension Assets) : Operating Asset * Op Asset beta = Equity MV * Equity beta 2, Total Asset beta*(Total Assets incl. Pension Assets) : Operating Asset * Op Asset beta2 + Pension assets * Pension Assets beta = Equity MV * Equity beta The two equations shall be valid at the same time. To keep Equity beta constant, Op Asset beta2 must be lower since all items are usually positive.

But, why not keep Op Asset beta constant? Then Equity beta will increase. Sponsoring a pension plan is like adding a risk for shareholders to me. It benefits plan participants, not shareholders…I get confused again.

equity beta is constant… it is the other way around. now with equity beta constant - because of the pension plan assets - your operating assets beta (risk) reduces. so now with that - you are better positioned to give the risk its due. without that - your operating assets are too risky, higher beta, higher WACC… (traditional without pension assets). with inclusion of pension assets - operating assets beta is lower - so WACC is more reasonable for all your projects evaluation… pension plan risk needs to be included appropriately to the pension assets - not to the operating assets .

Thanks. The firm also needs to take investment risk of pension plan. It helps the firm in good time, but it may make things worse in a market downturn?

I think I got it. Keeping equity beta constant is like the pension assets and liability have been priced in…The firm sponsors the pension plan whether to include it in the calculation or not. Thanks.

Yes, exactly. The market tells you the beta, it’s up to you whether you assume the beta communicated by the market incorporates the pension assets or not.

why does debt have a beta of 0? It’s uncorrelated with the equity markets? Surely interest rates have some correlation with the equity markets, no?

1.) why does debt have a beta of 0? BC it’s uncorrelated with the equity markets? Surely interest rates have some correlation with the equity markets, no?

2.) I don’t understand intuitively why increasing the risk of the pension plan increases the risk of operating assets? Why isn’t the increase in total asset beta attributable simply the result of higher plan beta, why does operating beta increase too? I see the math, but don’t conceptually get it.

part 1) Interest rate risk affects equity markets - not the other way around. Beta is related to systematic risk and it is the relation of the market to the relation of the global market = cov(rAsset, RMarket)/Variance (Market).

1. since your pension assets are being set aside to defease the liabilities and the pension assets and liabilities are now risk mismatched - and your operations are what is required to support the pensions in case the plan assets do not perform … if pension assets become more risky [this is because they are more invested in equities while your pension liabilities are more debt like] - your operating assets also become more risky.

Great points CPK, especially the second one. Hit the nail on the head. I feel like on the surface I understand the reading and it’s main points. It’s when I start getting into the weeds and trying to fully understand / track the impact on the various betas, etc is when I get confused.

One last question. With regards to modifying the capital structure if Mgt wants to maintain the same total equity beta when pension plan risk increases.

Does this also mean that as a result of changing the capital structure that the Operating Asset Beta also decreases?

I would think this is the case for two reasons:

a.) Pension Risk (beta) increases --> Total equity beta stays the same (bc of altered cap structure) --> then optg beta must decrease because the sum of a higher pension + lower optg beta = same total eequity beta

b.) By chaning the capital structure to have more equity & less debt, the risk of the operating assets all decreases bc more is back by equity

Is this logic and correct? Thanks