678 Part Eight Risk Management
bre44380_ch26_673-706.indd 678 09/30/15 12:09 PM
State Farm Insurance issued $300 million worth of Cat bonds. The bonds cover State Farm for
three years against any losses in excess of a specified level resulting from U.S. earthquakes.26-3 Reducing Risk with Options
Managers regularly buy options on currencies, inter-
est rates, and commodities to limit downside risk.
Consider, for example, the problem faced by the
Mexican government. Thirty percent of its revenue
comes from Pemex, the state-owned oil company.
So, when oil prices fall, the government may be
compelled to reduce its planned spending.
The government’s solution has been to arrange
an annual hedge against a possible fall in the oil
price. For example, in late 2014 the Mexican gov-
ernment bought put options that gave it the right to
sell 228 million barrels of oil over the coming year
at an exercise price of $76.40 per barrel. If oil prices
rose above this figure, Mexico would reap the ben-
efit. But if oil prices fell below $76.40 a barrel, the
payoff to the put options would exactly offset the
revenue shortfall. In effect, the options put a floor
of $76.40 a barrel on the value of its oil. Of course
the hedge did not come free. The Mexican govern-
ment was reported to have spent $773 million to buy
the contracts.
Figure 26.1 illustrates the nature of Mexico’s
insurance strategy. Panel (a) shows the revenue
derived from selling 228 million barrels of oil. As
the price of oil rises or falls, so do the government’s
revenues. Panel (b) shows the payoffs to the govern-
ment’s options to sell 228 million barrels at $76.40
a barrel. The payoff on these options rises as oil
prices fall below $76.40 a barrel. This payoff exactly
offsets any decline in oil revenues. Panel (c) shows
the government’s total revenues after buying the put
options. For prices below $76.40 per barrel, rev-
enues are fixed at 228 × $76.40 = $17,419 million.
But for every dollar that oil prices rise above $76.40,
revenues increase by $228 million. The profile in
Panel (c) should be familiar to you. It represents the
payoffs to the protective put strategy that we first
encountered in Section 20-2.^10(^10) The Mexican government option position was slightly more complicated than our description. On some of the production, it agreed
to take a hit if prices fell below $60 a barrel. On this portion of production, government revenues were protected only against prices
between $60 and $80.
Revenue, $ billions
$76.40
$17.419
(a)
Price per barrel
Sell 228 million barrels
of oil at market price
Revenue, $ billions
$76.40
$17.419
(c)
Price per barrel
5 lock in minimum
price of $76.40 a barrel
Revenue, $ billions
(b)
Price per barrel
buy put options
with $76.40 exercise price
- $17.419
$76.40
◗ FIGURE 26.1
How put options protected Mexico against a fall in oil
prices.