# 2.4: Risk Measurement and Metrics(Exercises)

• Anonymous
• LibreTexts
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

1. The Texas Department of Insurance publishes data on all the insurance claims closed during a given year. For the thirteen years from 1990 to 2002 the following table lists the percentage of medical malpractice claims closed in each year for which the injury actually occurred in the same year.
Year % of injuries in the year that are closed in that year
1990 0.32
1991 1.33
1992 0.86
1993 0.54
1994 0.69
1995 0.74
1996 0.76
1997 1.39
1998 1.43
1999 0.55
2000 0.66
2001 0.72
2002 1.06

Calculate the average percentage of claims that close in the same year as the injury occurs.

2. From the same Texas Department of Insurance data on closed claims for medical malpractice liability insurance referred to in Problem 1, we can estimate the number of claims in each year of injury that will be closed in the next 16 years. We obtain the following data. Here the estimated dollars per claim for each year have been adjusted to 2007 dollars to account for inflation, so the values are all compatible. Texas was said to have had a “medical malpractice liability crisis” starting in about 1998 and continuing until the legislature passed tort reforms effective in September 2003, which put caps on certain noneconomic damage awards. During this period premiums increased greatly and doctors left high-risk specialties such as emergency room service and delivering babies, and left high-risk geographical areas as well causing shortages in doctors in certain locations. The data from 1994 until 2001 is the following:
Injury year Estimated # claims Estimated $per claim 1994 1021$415,326.26
1995 1087 $448,871.57 1996 1184$477,333.66
1997 1291 $490,215.19 1998 1191$516,696.63
1999 1098 $587,233.93 2000 1055$536,983.82
2001 1110 $403,504.39 1. Calculate the mean or average number of claims per year for medical malpractice insurance in Texas over the four-year period 1994–1997. 2. Calculate the mean or average number of claims per year for medical malpractice insurance in Texas over the four-year period 1998–2001. 3. Calculate the mean or average dollar value per claim per year for medical malpractice insurance in Texas over the four-year period 1994–1997 (in 2009 dollars). 4. Calculate the mean or average dollar value per claim per year for medical malpractice insurance in Texas over the four-year period 1998–2001 (in 2009 dollars). 5. Looking at your results from (a) to (e), do you think there is any evidence to support the conclusion that costs were rising for insurers, justifying the rise in premiums? 3. Referring back to the Texas Department of Insurance data on closed claims for medical malpractice liability insurance presented in Problem 5, we wish to see if medical malpractice was more risky to the insurer during the 1998–2001 period than it was in the 1994–1997 period. The data from 1994 until 2001 was: Injury year Estimated # claims Estimated$ per claim
1994 1021 $415,326.26 1995 1087$448,871.57
1996 1184 $477,333.66 1997 1291$490,215.19
1998 1191 $516,696.63 1999 1098$587,233.93
2000 1055 $536,983.82 2001 1110$403,504.39
1. Calculate the standard deviation in the estimated payment per claim for medical malpractice insurance in Texas over the four-year period 1994–1997.
2. Calculate the standard deviation in the estimated payment per claim for medical malpractice insurance in Texas over the four-year period 1998–2001.
3. Which time period was more risky (in terms of the standard deviation in payments per claim)?
4. Using the results of (c) above, do you think the medical malpractice insurers raising rates during the period 1998–2001 was justified on the basis of assuming additional risk?

This page titled 2.4: Risk Measurement and Metrics(Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Anonymous.