Availability premium

The term availability premium or convenience yield is the income that the owner of a good accrues from his possession in times of imminent and actual storage bottlenecks. According to Nicholas Kaldor, the convenience yield does not include any appreciation of the property.

The convenience yield describes an adjustment in the cost of carry model. It is the variable that ensures that inverse date structures are found in raw materials and is an explanatory variable in the "Theory of Storage".

The "Theory of Storage", the original concept of which was taken up by Nicholas Kaldor (1939), aims to explain the differences between spot and future prices by trying to analyze why traders hold stocks (Geman, 2005). During the development of this theory, the need to include actual stock levels and production quantities in the explanation was highlighted.

Distinction

With regard to the production of goods, Kaldor differentiates between two types of goods: durable goods and consumer goods. In the case of consumer goods, which include raw materials, the possibilities to reduce or build up stocks can be very limited in certain situations. Therefore, the convenience yield of these goods falls or rises sharply in certain situations. This is not the case with consumer goods. In the following only consumer goods - raw materials - are considered. Kaldor (1939) and Working (1949) describe the convenience yield as revenue that goes to the owner of a raw material. Here you could compare the convenience yield with the dividend of a share. Brennan (1958) and Telser (1958) see the convenience yield more as a kind of option that allows the owner to sell a commodity when prices are high enough. The convenience yield can also be seen as a safeguard against production downtimes, since a company that consumes raw materials can only work continuously if it has the necessary raw materials (Geman, 2005).

No arbitrage

The arbitrage-free relationship between the spot and the future price in connection with the convenience yield, which here clearly has the property of the dividend of a share, will now be explained. The model of the procedure is based on Geman, Commodities and commodity derivates, 2005 (stocks were used there). Let us assume that today you buy a commodity at a price and borrow the money you need for a risk-free interest rate of for a period of . In addition, you sell a future on exactly this commodity (with the corresponding quantity, expiry date, etc.) . For the sake of simplicity, it is assumed here that the convenience yield and storage costs are zero. Then you get the following strategy: ${\displaystyle i\ }$ ${\displaystyle S_{\text{it}}\ }$ ${\displaystyle r_{tT}\ }$ ${\displaystyle T-t\ }$ ${\displaystyle F_{itT}\ }$

	t	T
Purchase of the raw material ${\displaystyle i}$	${\displaystyle -S_{\text{it}}\ }$	delivery
Borrowing	${\displaystyle +S_{\text{it}}\ }$	${\displaystyle -S_{\text{it}}e^{r_{\text{tT}}(T-t)}}$
Sell ​​Future	${\displaystyle -\ }$	${\displaystyle +F_{\text{itT}}\ }$

It is important here that all cash flows that are generated at the end of the period are independent of the spot price , which is stochastic. This is a risk-free strategy that is also free of arbitrage. Since it has a value of zero at the point in time , it must also have this at the end of the period due to the freedom from arbitrage . Therefore the following relationship applies: ${\displaystyle S_{\text{iT}}}$ ${\displaystyle t}$

${\displaystyle F_{\text{itT}}=S_{\text{it}}e^{r_{\text{tT}}(T-t)}}$

The continuous convenience yield is now being introduced. For reasons of clarity, it is defined as the net convenience yield that applies to the period of . This means that the storage costs are deducted from the gross value . The holder of the raw material receives the continuous convenience yield over the period . One assumption that will certainly be difficult to confirm in reality is that this convenience yield will now be continuously reinvested. This would mean that, firstly, a convenience yield is paid out immediately (questionable) and, secondly, you can actually physically buy a certain share of a raw material immediately (questionable). ${\displaystyle c_{\text{tT}}^{N}}$ ${\displaystyle T-t\ }$ ${\displaystyle c_{\text{tT}}\ }$ ${\displaystyle w_{\text{tT}}\ }$ ${\displaystyle (t,t+dt)\ }$ ${\displaystyle c_{\text{tT}}^{N}S_{\text{it}}dt}$

Due to the continuous reinvestment, the growth of our assets now corresponds . To make the arbitrage relationship clear, a raw material is bought for in . ${\displaystyle e^{c_{\text{tT}}^{N}(T-t)}}$ ${\displaystyle -e^{-c_{\text{tT}}^{N}(T-t)}S_{\text{it}}}$ ${\displaystyle t\ }$

	t		T
partial purchase of raw material ${\displaystyle i}$	${\displaystyle -e^{-c_{\text{tT}}^{N}(T-t)}S_{\text{it}}}$	cont. Reinvest. in ${\displaystyle i}$	Receiving 100% of the raw material
Borrowing	${\displaystyle +e^{-c_{\text{tT}}^{N}(T-t)}S_{\text{it}}}$	${\displaystyle -\ }$	${\displaystyle -S_{\text{it}}e^{(r_{\text{tT}}-c_{\text{tT}}^{N})(T-t)}}$
Sell ​​Future	${\displaystyle -\ }$	${\displaystyle -\ }$	${\displaystyle +F_{\text{itT}}\ }$

Again, it is a risk-free, arbitrage-free business. The relationship between the future price and the spot price can now be represented as: ${\displaystyle c_{\text{tT}}^{N}=c_{\text{tT}}-w_{\text{tT}}}$

${\displaystyle F_{\text{itT}}=S_{\text{it}}e^{(r_{\text{tT}}+w_{\text{tT}}-c_{\text{tT}}){(T-t)}}}$

With this connection, the two (pure) states of an appointment structure can be explained. A date structure is either in contango (normal) if the prices of the near-term expiration dates are lower than those of the distant expiration dates. Or it is in backwardation (inverse) when the increased convenience yield due to an impending sell-off ensures that the prices of the near-term expiration dates are higher than those of the distant ones.

literature

• N. Kaldor: Speculation and economic stability. In: The Review of Economic Studies. 7, 1939, pp. 1-27
• H. Working: The theory of the price of storage. In: American Economic Review 39, 1949, pp. 1254-1262
• MJ Brennan: The supply of storage. In: American Economic Review. 48, 1958, pp. 50-72
• LG Telser: Futures trading and the storage of cotton and wheat. In: Journal of Political Economy. 66, 1958, pp. 233-255
• H. Geman: Commodities and commodity derivatives. 2005