This paper examines the apparent failure of private markets to adequately insure long-term risks. I argue that the key to long-term insurance is the importance of intertemporal risk. Long-term risks are difficult to insure because much of the risk concerns variability in the average cost of services used, rather than cross-section heterogeneity in service use. When intertemporal risk is large, insurance will provide indemnity benefits rather than a service benefit, and this in turn will limit demand for insurance. Analysis of long-term care insurance supports this view. An insurer underwriting full long-term care insurance would have a standard deviation of average costs for its pool of policies of 13 percent. Full insurance is essentially non-existent, however. Rather, insurers offer an indemnity payment conditional on use. While I cannot directly test whether this indemnity payment limits demand, I show that other common theories of market failure cannot explain all of the low rate of insurance purchase.