Optimal Leverage Strategy

The concept of the correct amount of leverage comes up frequently on the BP forums.  Many advocate a staunch conservative position while others think that money stuffed in projects can be used better elsewhere.  Occasionally someone comes on the forums and asks about the “proper” amount of leverage.  There is generally a back and forth for a while without sufficient thought given to many of the key variables needed to advise the original poster.

I have struggled with the concept of an optimal leverage point for years now.  We are rather conservative with our portfolio and would like to keep our ratios in the proper range to continue borrowing, eliminate default risk to the maximum degree possible, and keep things in a range that lets us sleep at night.

So where can one look for guidance on this issue if the forums of many experienced investors don’t produce good advice?  Prior to joining BP I found an article about optimal leverage strategy by Roger E. Cannaday from the University of Illinois.  Being the engineering nerd that I am I pieced together the arguments in the article.  Partial differential equations, items subject to maximal constraints, etc. are all used to demonstrate the following:

-The interest rate of a mortgage loan is usually positively related to the desired LTV ratio.  This is because the lender demands additional return for the level of risk associated with the loan.  As LTV increases the likelihood of default increases

-The optimal LTV increases as the marginal tax rate of the investor increases

-The higher the required ROE, the more the investor will borrow

-Investors are heterogeneous with different risk preferences, marginal costs of equity, etc. and will arrive at different required rates of return for the same investment.  Greater risk aversion by a particular investor will drive a higher required ROE for a given level of risk

The article goes on to define some pretty involved equations to describe all of this in math-land absent any of the chaos the real world yields.  There are other interesting conclusions as well, but the bullets above are the bulk of what is described.

So what conclusions can we draw from this?  People with higher marginal tax rates should borrow more because they can take advantage of the higher tax shields.  Lenders want higher interest rates if they kick in more for acquiring the investment because you are more likely to walk away from the loan.  If you want to increase your ROE and demand a higher ROE to do projects you have to borrow more to increase your yield.  People all have different needs, timelines, etc. and thus rational investors can arrive at different prices for assets because of this heterogeneity. 

Well thanks researcher guys.  We didn’t really need a bunch of equations to figure that out.  As leverage in my portfolio grows how do I figure out how to account for my risk aversion in your equations?  That is pretty tough to model with some equations. 

The truth is that you can’t really do it very well.  However, in general your leverage ratio should decrease as you age.  This is consistent with a heightened risk aversion and the general principle that you have a shorter timeframe until you need to monetize the asset.  It remains a mystery to me how one comes up with an optimal ratio though.  If readers know of good resources for this I would love to see them.