Topic 10 – Convenience Yield and Storage Logic (Power vs Other Commodities) — Desk–Quant Dialogue Playbook

1. Cost-of-carry picture: how forwards link to spot

For a storable commodity (oil, gas, metals), a standard cost-of-carry relation is:

$F(0,T) = S_0 \, e^{(r + u - y)T}$

where:

$S_0$ : spot price today.
$F(0,T)$ : forward price for delivery at $T$ .
$r$ : risk-free rate (funding cost).
$u$ : storage cost rate (rent, insurance, losses).
$y$ : convenience yield (benefit of holding the physical).

Rearranged:

$\ln\frac{F}{S_0} \approx (r + u - y)T$

So net carry = $r + u - y$ .

If net carry > 0 → forwards tend to be above spot (contango).
If net carry < 0 → forwards tend to be below spot (backwardation).

2. What is “convenience yield” in words?

Convenience yield = non-cash benefit of owning physical inventory.

Think of it as:

“Shadow dividend you get from having the stuff now rather than only having a contract for later.”

Examples of benefits:

Ability to satisfy unexpected demand or contractual obligations.
Protection against supply disruptions or logistics issues.
Operational flexibility: blending, quality control, using the “good” barrels first.
Avoiding stockouts, which can be far more expensive than storage costs.

When inventories are tight:

Extra unit of stock is very valuable (you avoid shutdowns, penalties, lost sales).
Convenience yield $y$ is high.
Formula: r+u−yr + u - y can become negative → backwardation:
- Spot > forwards, because holding now is more valuable than promising later.

When inventories are plentiful:

Extra stock gives little extra benefit.
Convenience yield is low.
Net carry r+u−yr + u - y is positive → contango:
- Forwards above spot; it’s relatively cheap to buy and store for later.

3. Storage arbitrage intuition

Try to see the two classic trade directions:

3.1 Cash-and-carry (contango exploitation)

If:

$F(0,T) \gg S_0 \, e^{(r + u)T}$

then roughly $y \approx 0$ but forward too high.

Strategy:

Today:
- Borrow money at rate $r$ ,
- Buy spot at $S_0$ ,
- Store (pay storage cost $u$ ),
- Sell forward at $F(0,T)$ .
At TT:
- Deliver spot into forward,
- Repay loan + storage.

If forward is “too high”, this locks in risk-free profit: cash-and-carry arbitrage.

3.2 Reverse cash-and-carry (backwardation exploitation)

If:

$F(0,T) \ll S_0 \, e^{(r + u)T}$

then forward is “too cheap”.

Strategy:

Today:
- Sell physical inventory (or short spot),
- Invest proceeds at rate $r$ ,
- Buy forward for $T$ .
At TT:
- Use proceeds to pay forward,
- Receive physical back.

If the forward is cheap relative to spot + carry, you harvest the difference.

In equilibrium, these trades bound the relationship between spot, forward, carry, and convenience yield.

4. Why power is special

Electricity is hard to store directly:

Batteries exist but are expensive and limited.
Most power systems still rely on instant balancing of supply and demand.
Physical “inventory” is more like:
- Fuel in tanks (gas, coal, oil),
- Water in reservoirs (hydro),
- The ability to produce (capacity, ramping, flexibility).

So for power:

The classic cost-of-carry formula in terms of power spot storage is not natural.
Convenience yield is more attached to:
- Having fuel inventory,
- Having reservoir water,
- Having flexible capacity (peakers, batteries, demand response).

This is why in practice:

We mainly look at forward curves in power (months, quarters, years).
Spot is a spiky, delivery-based index (e.g. day-ahead / intraday auctions).
“Storage-like” optionality lives in:
- Gas storage, hydro reservoirs, batteries, demand-side flexibility.
Convenience yield appears as:
- Spread between forward prices and “implied” cost from fuels + CO₂ + capacity.

5. Relation to inventories and market regimes

For oil/gas/metals:

High inventories:
- Storage tanks full, low risk of shortage.
- Low convenience yield → forwards often in contango.
Low inventories:
- Tanks low, risk of outages / rationing.
- High convenience yield → forwards often in backwardation.

For power:

We look at fuel and hydro inventories instead:
- Gas storage levels ahead of winter.
- Hydro reservoir levels vs long-run averages.
High fuel/water levels → “comfortable” system, winter risk lower.
Low fuel/water → risk of spikes if winter is harsh → forward curve steepens.

Interview sentence:

“In storable commodities, convenience yield captures the non-cash value of holding inventory: security of supply and operational flexibility. High convenience yield tends to produce backwardation. Power is different: we can’t store electricity easily, so convenience yield mostly lives in fuels, hydro reservoirs, and flexible capacity, not in power spot itself.”

6. How this connects to term structure and optionality

Term structure shape (contango/backwardation) is a summary of:
- Funding, storage, and convenience yield.
Structured products (storage, swing, tolling) are options on these economics:
- Inject when spot + carry < future; withdraw when spot > forward.
- Exercise decisions depend on convenience yield and expected future shapes.

So as a quant dev:

Pricing libs must support:
- Cost-of-carry-style projections,
- Inventory-linked state variables (storage level, reservoir),
- Path-dependent optimisation.
Risk libs must expose:
- Sensitivity to curve level,
- Sensitivity to curve shape and spreads (calendar, location, spark).