What is the opportunity cost of holding gold? An educated guess.
A previous post pointed out that from a central bank’s perspective gold could be considered in a loose sense as a floating rate perpetuity or a dividend paying share – where the lease rate is the equivalent of a dividend. However if we were to value gold by discounting its future cashflows we would need to decide what we believe is gold’s Opportunity Cost of Capital.
Finance 101 courses teach that the Opportunity Cost of Capital is the best alternative investment opportunity foregone, at a similar level of risk. So for a central bank if we will simplify and say they are investing in gold for leasing cashflows and capital appreciation, what investments are available at a similar level of risk?
First let’s look at alternative investments in bonds.
Some writers say that as gold can’t default it is a risk free investment. If we accepted this we would use a short term government interest rate, like the 3 or 6 month UST-bill rate. This perspective is based the fact on gold will always be gold no matter what happens to the economy. But here we are concerned with the value of gold in an investor’s portfolio and a brief look at a gold price chat over the last few years it should be clear that owning gold in your portfolio it is not risk free, $1800 gold wasn’t that long ago.
Gold is default risk free for average investors but only because it doesn’t promise to pay anything. Not too big of a claim to make. We can use these risk free rates to value gold but because they relate to a lower risk investment they will bias the results towards over valuation. Current 3m US T-Bills yield just over 0.25%.
LBMA documents indicate that the gold leasing market has never suffered a default so we can think of the probability of defaulting on a leasing payment as being very low, similar to the likelihood that major banks would default on loans to each other. So the London Interbank Offer Rate (LIBOR), despite its well publicised failings, seems the best candidate for an Opportunity Cost of Capital for gold if we think its like a bond of some sort. Todays 6 month Dollar LIBOR is around 0.75% and 12 month is just over 1.25%.
An issue with using LIBOR is that when there is a significant increase in the risk of an interbank default the rate rises and this would push the price of gold down in a discounted cashflow model – precisely when gold value would be expected to increase due to its safe haven characteristics..
We can also look at alternative investments in equities.
One way to calculate the opportunity cost of holding a stock is to get it’s Beta – it’s relationship with a market index calculated from the Capital Asset Pricing Model (another a Finance 101 idea). I calculate gold’s beta at about -0.11 which means that a 10% increase in the S&P500 index is associated with a -1.1% change in the US Dollar gold price and vice versa. This negative relationship is what we would expect and is shown below between 1989 and 2015 on a monthly average basis.
The issue is that this beta implies that gold is about 1/10th as risky an investment as a diversified portfolio of stocks which doesn’t seem entirely credible. Both have very similar standard deviations and the chart shows big variations in both. It also shows long periods where gold prices and the S&P500 moved together broadly – 2003 to 2008 for example, its possible that Beta is being influenced strongly by safe haven periods where gold holds it’s value while stocks fall.
Beta, to me, seems a better indication of gold’s ability to diversify a portfolio rather than calculate a cost of capital to use in a valuation. But if we did accept it as a useful measure then the average annual return on the S&P500 over that period has been 6.9% so that the cost of capital for gold would be about 0.98%.
Both ways of measuring gold’s opportunity cost of capital are wrong in a pure sense as it isn’t really a bond or an equity. It doesn’t pay Par Value like a bond or a fixed coupon like a perpetuity. And unlike the company behind the share the likelihood that gold will stop existing in the future is not a significant one. But they do give an educated guess that the current cost of capital for gold is somewhere between 0.25% and 1.25% depending on the assumptions you make.