Yes, I know I am a but behind on my academia postings, but looking into models has kept me up at night (models for the Asian economies, mind you). I thought sharing some of these findings with you might be more interesting, particularly as they deal with some of the most important data points available in finance.
Remember how I wanted to model cost of equity capital for Asian economies after the insight into their debt breakdowns allowed me to evaluate how much debt costs these economies? Well it turned out that this wasn’t particularly easy, to say the least. And no, I’m not one to give up particularly early, so after finding out that CAPM had to go out the window, I decided to try my hand at making a fledgling of a model of how much equity capital contributes to economic growth, and deduce the cost of equity capital from there.
Assumptions and introduction:
Ever heard that stock markets cannot grow faster in the long term than the economies underpinning them? Yeah, same here, I’m sick of hearing it. I think it’s the mathematical equivalent of saying that the stock price of a company has to go up in tandem with revenue – both ideas fundamentally ignore the capital structure. My approach starts at a slightly different area than raw cash flows – return on assets, and then goes through a DuPont-formula inspired process of estimating long-term expected return on equity. It hinges to a large extent on finding a rate that isn’t “all inflation” and then going through adjustments for inflation and economy-wide cost of debt to arrive at the growth attributable to equity capital. A side effect is that this has very little to do with GDP growth overall, and the model never once touches GDP in the calculations, although a “second pass” through the maths might reveal some places where GDP can replace the currently used variables.
For debt purposes, the government is assumed to only be a re-distributor of wealth in the long term (which assumes a balanced budget and very little efficiency losses in distributing money from the taxpayers to government spending). My qualitative rationale is that the government in most cases simply does this, can engage in short-term fiscal stimulus or tightening, but that this simply impacts the economy rather than changing long-term differential equation terms. Where they are able to do this – in legislating for more of less business friendliness, specific taxation structures, etc. – they don’t necessarily spend any money so it can’t really easily be modeled mathematically. Yield on government debt is simply seen as a cost that will need to be paid out of the surplus of the productive sectors of the economy. future revisions might include budget deficit / surplus levels (which would be an absolute necessity if I was to cast this as a long-term differential equation) but has been ignored at the moment to the benefit of drawing quickly computable results and producing a testable model.
Banks are roughly seen as having the same function as the government – redistributing money. Their surplus is more or less implicitly covered in the initial model steps and can easily befall the economy as a whole so separating out financial institution payouts isn’t something I am going gaga over.
- Government bonds are seen as costing the current 10Y yield for the foreseeable future. Forecasting this is the topic of books in their own right, feel free to plug in future government bond yield models if you have the data available and can run a decent model.
- Ditto inflation. I simply use an average of the 10Y yield and current inflation to estimate long-term inflation. It mostly gives me values across Asian markets that correlate heavily to my gut feeling, but you can change this at your leisure.
- Corporate bond yields are simply modeled as Y = [Gov. 10Y] * 1.3 + 30 bps in the long term. This should be really easy if you have the data to run regression on, but I couldn’t really be bothered across 10 economies and lacking of data at my fingertips. Again, it’s up to you to change it if you feel like it.
- Household loans and loans to corporates are seen simply as being held at the prime rate.
Step 1 – Find the yield of assets generally in the economy.
How much can an investment in an average asset claim on a real asset or equity throughout an economy be expected to pay off? At least enough that the investor can expect to cover the interest on a loan corresponding to the asset value, after covering his or her assumed risk and cost of associated operations and transactions. (This covers the bank earnings I mentioned earlier.) If the investor doesn’t borrow the money then of course the interest-related return should go directly to said investor anyway.
How much is this? At least the prime rate! The prime rate is given out from banks to secured lenders, be they companies or individuals. Still, additional capital buffer requirements for companies and down payment requirements for households, so the yield rate should be higher than the prime rate.
How much higher? This is where good plug-in models will generate additional value but historical regressions (had I been bothered to run them) are generally pretty useful. In the interest of actually being done in time and not writing a PhD thesis I opted for a very simple model:
Ry = A + Rp * B
This is basic regression with Ry being the yield rate, Rp being the prime rate, and A and B being positive regression coefficients. Since I didn’t do regressions, I manually put A between 1.05-1.2 with an additional bonus for China and India (big growth economies), and B somewhere around 0.5-1.5% in after-adjustments.
Step 2 – Identify asset values that this applies to.
Again a relatively simple model (hinted at in the assumptions), I simply plugged in non-government debt plus equity market capitalization to represent financial asset values. The equity market capitalization in a way leapfrogs book value of equity in the economy, but as an investor I have little interest in book value of the shares I buy if I know the real rate of return I can expect on the stocks I look into.
For real assets, the modeling is a lot more annoying and complicated, but the same general yield rate idea applies. Here I simply highjack my prior assumptions on how well-amortized loans in different economies are based on a visual inspection of charts of loan growth, apply that feeling to a 30-year fixed amortization repayment plan to evaluate how much of the household assets are represented by the household loans, and then apply the prior yield rate to household assets.
- I then multiply this by 1.5 to account for assets used by the private sector but held by a bank or other entity whose balance sheet would not be accessible in this analysis. The 1.5 factor is obviously pulled from thin air, but would most likely require combing through aggregated bank balance sheets and deep looks into their various asset-backed lending portfolios to get a better grasp of. Can I be bothered with this over 10 economies and not being paid for it? Nope!
- Obviously, better assessment of the average maturity of loans and mortgages will improve this analysis, but that is also a big bank financial statements-dive I’m not ready for at the moment.
- Ideally, a lag factor should be applied to this, since not everyone will refinance their houses as soon as the property prices go up a teeny little bit and then spend that money, if at all. Alas, this requires a bit more research (again) than I think it’s worth at the moment on several economies at once, but if you’re looking into a specific economy finding research that can plug this analytical hole shouldn’t be too bad of a Google search away.
Step 3 – Calculate the long-term inflation-adjusted yield rate of these assets.
Ygr = Assets * (1 + Ry) / (1+LTI)
Pretty straightforward! Ygr: gross real yield. LTI: expectation for long-term inflation.
Step 4 – Subtract all interest costs in the economy.
YTE = Ygr – ∑[size of sum of loans of type i] * [interest on loan type i]
Sum over all i. YTE: Yield-to-Equity. As previously mentioned, government debt costs are covered here, since they need the private sector earnings to tax for then paying off the debt. household debts are simply measured at their current rather than initial value (you pay interest on the current portion) and both that and corporate loans are expected in my models to have a maximum average prime rate on the foreseeable future 5% higher than current prime rates. You might want to change the cost of government bonds dynamically depending on how much refinancing the country will need to do in the near future and how long ago debt of what maturity was raised. Again, no data and even less energy to look it up.
Step 5 – Divide by YTE by current equity market capitalization.
You might want to adjust this to any models used for “fair value” estimations of the stock markets in the country/countries you are interested in. Finished!
This approach essentially takes something inflation-related – the prime rate – includes it in the analysis and then readjusts data first for inflation of the underlying assets, then for the cost of interest on the loans that have been used to buy these assets. We’re running laps around inflation here!
If the government holds massive assets, this analysis doesn’t account for them well enough, but it is slightly questionable if these gains would befall the private sector in the short-to-medium term anyway unless the government sells those assets and pays debt back or lowers taxes for the foreseeable future.
This analysis looks at the long-term rate, or terminal required rate of return. Normal non-terminal time-segmented required rates of return and similar growth rates are still as you practiced for the CFA 1 for whatever “non-forever” time you’re looking into.
Additional debt- or equity capital raising in the future is ignored. I expect that current expectations have already accounted for this to the extent that it is possible.
As with all analysis, this is highly input-sensitive. Change a little bit of the inflation rate, and you will get radically different results. If the yield rate Ry changes, then we are in for a rodeo-ride of evaluation changes.
This is not a dynamically-adjusting long-term model, which would necessitate it being a partial differential equation with a lot of the intermediate and related outputs that this model gives being fed back in. (Long term asset formation rate, long term debt inflation factor, long term refinancing rate of consumer debt, government deficit expectations, etc.) I might come back to this at some point, but it’s not very likely given all the required research and empirical PDE parametrization that it would imply if you’re gonna hear anything else than “I couldn’t bloody be bothered researching anything!”
Wanna play around a bit with the models yourself? Think you can plug better models for key variables than I have? I have a decently presentable excel sheet just for you. (I never clean my excel sheets, consider yourself lucky!) Feel free to use this excel workbook, model the results and tell me in the comments what your projected economies look like: Asian CoE est
I might drop in from time to time with more use of this data sheet, mainly to try and figure out just how much actual aggregate financing (rather than just debt) costs are going through the economies here.
Note: Keep in mind, the excel sheet is done to extract data, so a few extra hoops were jumped through to not report real numbers, but GDP fractions. This is mostly for my own good later, but the extra data isn’t so hard for you to look into on your own.