BRAUCHER, J.

We here review the decision of the Commissioner of Insurance (Commissioner) fixing industry-wide automobile insurance rates for the calendar year 1980 pursuant to G.L.c. 175, § 113B. We uphold the Commissioner's decision with respect to the allowances for losses and expenses, but remand for further consideration of the allowance for profit.

1. The present proceeding. The Commissioner held a hearing in May, 1979, pursuant to G.L.c. 175E, § 5, and determined that competition was insufficient to assure that rates would not be excessive. He therefore undertook to fix 1980 rates pursuant to his traditional authority under G.L.c. 175, § 113B. See American Mfrs. Mut. Ins. Co. v. Commissioner of Ins., 374 Mass. 181, 184 (1978). Hearings began on September 24, 1979, and produced a voluminous record. The Commissioner issued his decision on December 20, 1979. The Massachusetts Automobile Rating and Accident Prevention Bureau (Bureau), an unincorporated association of insurance companies writing motor vehicle insurance in the Commonwealth, and eighty-six named insurance companies filed a complaint seeking review in the Supreme Judicial Court for Suffolk County. A single justice of this court reported the case without decision for determination by the full court.

The Bureau filed proposed rates on behalf of the industry requesting an over-all rate increase of 20.6%. Formal rate filings were also made by the Attorney General and by the Division of Insurance (Division). Also participating were two associations of insurance agents, the National Consumer Law Center, the Massachusetts Bay Transportation Authority, the Car and Truck Rental and Leasing Association, Massachusetts Fair Share, and the Massachusetts Consumers' Council. The Bureau asserts that the rates fixed by the Commissioner, which produce more than $700 million, provide an over-all increase of 5.7%, some $100 million less than the Bureau's request.

2. Background. The decisions of the Commissioner as to 1978 and 1979 rates were made part of the record in the present case. Those decisions review the developments of the past few years. In 1975 some of the largest underwriters announced that they were contemplating withdrawal from the Massachusetts market; notices of impending cancellations of policies were sent to agents and brokers. The insurers claimed that the rates set for 1976 were inadequate and sought some $132 million in additional rates, but this court upheld the Commissioner's decision. Attorney Gen. v. Commissioner of Ins., 370 Mass. 791 (1976) (our 1976 decision). Data subsequently accumulated showed that in 1976 "Massachusetts was the most profitable state in the entire country for automobile insurance underwriting."

Rates for 1977 were increased by about 14.5% under a system of "competitive" rate setting, despite a recommendation by the Division that there be no over-all increase. By the middle of 1977 the perception became widespread that the rates were excessive, and the Legislature enacted a reduction of the 1977 rates, which we upheld against constitutional attack. American Mfrs. Mut. Ins. Co. v. Commissioner of Ins., 374 Mass. 181 (1978). In his opinion on the 1979 rates the Commissioner stated that the Division's recommendation for 1977 had been "close to target."

In fixing 1976 rates the Commissioner adopted a novel procedure for determining the profit allowance. Traditionally, that allowance had been set at an arbitrary 1% of total premium for compulsory coverages and 5% of total premium for other coverages. That method failed to take adequate account of the income from investing the cash flow of premiums received and not yet paid out in losses and expenses. The procedure substituted by the Commissioner was described and upheld in our 1976 decision. 370 Mass. at 812-822. We noted that the approach was "not only novel but complicated, and that somewhat greater imprecision must be tolerated in its initial application than might be acceptable in later years." Id. at 820. In the present case the Commissioner used a similar procedure, but changes have been made on the basis of the work of Dr. William Fairley, for several years a staff member of the Division.

3. Procedural issues; supplementary affidavits. The Bureau and the insurers attack the Commissioner's decision on both statutory and constitutional grounds, and three of the insurers make an additional claim of confiscation based on their individual underwriting losses. Our decisions say that we are to determine whether the rates set by the Commissioner have "reasonable support in the evidence." When a claim of unconstitutional confiscation is made, we are to make an independent determination of the facts as well as the law. Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 795 n. 4 (1976). But we are not required to hear the evidence ourselves. Zussman v. Rent Control Bd. of Brookline, 371 Mass. 632, 636 (1976). Independent review does not extend to subsidiary findings by an agency whose action is under review, and the agency action will be examined with the "presumptive validity" ordinarily attaching to it. Greenleaf Fin. Co. v. Small Loans Regulatory Bd., 377 Mass. 282, 301 (1979), and cases cited.

As a corollary of independent review of facts in public utility rate cases, we have followed a practice of allowing supplementary affidavits to bring the proof as nearly as reasonably possible down to the date of final decision. See Boston Edison Co. v. Department of Pub. Utils., 375 Mass. 1, 8-9, appeal dismissed, 439 U.S. 921 (1978), and cases cited. Purporting to follow that practice, the plaintiffs submitted five affidavits. The single justice included in the record these affidavits, together with two responding affidavits by the Commissioner and by the director of the State Rating Bureau in the Division, without decision as to their admissibility or materiality. One of the plaintiffs' affidavits purports to show industry-wide underwriting losses in 1978 and greater projected losses for 1979 and 1980; it also includes motor vehicle accident and death statistics compiled by the Registry of Motor Vehicles and a study by the Commissioner of Probation of driving under the influence of liquor. Three affidavits purport to show underwriting results for each of three insurance companies. The fifth affidavit purports to show investment income and operating results for the three companies and for the industry for the same three years.

We have examined the affidavits, and we conclude that we should not consider them. Rates are made on the basis of the combined experience of all companies doing business in the Commonwealth, and judicial review does not depend on a claim that the premium charges will be confiscatory as to any particular company. See Insurance Rating Bd. v. Commissioner of Ins., 359 Mass. 111, 115 (1971). Rates are not confiscatory merely because aggregate collections are not sufficient to yield a reasonable profit to all the companies unless it is shown that the business is so well and economically organized and carried on as to entitle the plaintiffs, as a matter of constitutional right, to have premiums amounting in the aggregate to enough to yield a reasonable return to all companies. Greenleaf Fin. Co. v. Small Loans Regulatory Bd., 377 Mass. 282, 301 (1979). The plaintiffs have not made the necessary showing of efficiency either with respect to the entire industry or with respect to particular companies.

Moreover, the information contained in the plaintiffs' affidavits is different in kind from the information considered in the public utility cases relied on. In those cases the affidavits typically supplied updated financial results, not available when the administrative hearings closed, in the same format relied on in the administrative decision. Sometimes they supplied actual figures for such items as a tax increase, a wage increase, or cost of debt, which could only have been estimated on the administrative record. The information was highly material, could not have been presented at the administrative hearing, and was easily verifiable. The affidavits in the present case include much information that was available at the time of the hearing; and that information and the subsequent information, projections and estimates are presented on the basis of methods and data rejected by the Commissioner. Verification would involve an entire new rate hearing.

4. Allowance for losses. The Commissioner began his estimation of 1980 losses with reported loss experience for 1978, adjusted by "development factors" to arrive at the expected final loss experience for 1978. "Trend" and "projection" factors were then used to take account of actual and expected changes in price levels after 1978. See Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 796-797 (1976). There is now no dispute as to the 1978 loss experience or development factors. But the Bureau claims error with respect to a number of other adjustments to take account of changes in claim costs and frequency relating to appraisals of property damage, accelerating inflation, drinking age, the tort threshold, merit rating, and worsening loss experience in 1979.

a. Appraisals. Effective September 1, 1978, the Division promulgated Regulation 1-78, a set of rules designed to reduce losses by improving practices in the appraisal and repair of motor vehicles. In most respects the Commissioner accepted the Bureau's estimates of resulting loss savings, but the Bureau objects to savings attributed to the provisions of the Regulation relating to licensing and supervision of appraisers. In his decision on 1979 rates, the Commissioner rejected the Bureau's contention that those provisions would produce no savings, but accepted the Bureau's argument that the benefits would take time; hence he projected savings of .5% in place of 4% recommended by the Division for collision coverages and assumed no savings at all for comprehensive coverage. In the hearings on the 1980 rates the Bureau introduced evidence that some of the major companies, accounting for more than 50% of the market, had long had internal standards similar to the requirements of the Regulation; it now argues that there was no evidence of improved qualifications of appraisers or of action to enforce higher standards. The Division pointed to an increase from 1978 to 1979 in the difference between body shop estimates and company appraisals, attributing the increase to improvement in the quality of appraisals. Despite weaknesses in this evidence, we cannot say that the Commissioner's finding that the Division's projection was "more realistic" was without reasonable support in the evidence. Even when loss estimates are very reliable, "their projection into the future is to some extent a matter of prophecy." Massachusetts Bonding Ins. Co. v. Commissioner of Ins., 329 Mass. 265, 277 (1952). Compare Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 805 (1976) (in the absence of evidence on the "body-shop overpayment problem," "the Commissioner's comment becomes speculation concerning a matter of fact and it cannot form an adequate foundation for decision").

b. Accelerating inflation. The Bureau proposed that trend factors for all coverages be increased by a "supplemental trend factor" to reflect acceleration in the rate of inflation. The proposal was based on an econometric projection of the rate of inflation by the Congressional Budget Office, based on the Consumer Price Index — All Items. The Commissioner found that that index did not track with changes in specific cost indices such as Auto Repair, and that certain items, such as energy costs, would have a delayed impact on losses. He therefore rejected the Bureau's proposal; instead, he used updated cost indices to recalculate the trend factors, as proposed by the Bureau, with a marked upward impact. Thus the Commissioner did not ignore the fact of inflation. Compare New England Tel. Tel. Co. v. Department of Pub. Utils., 371 Mass. 67, 73-74 (1976). We cannot say that he was in error in relying on observed facts with respect to specific types of costs rather than on a more general econometric projection. Massachusetts Bonding Ins. Co. v. Commissioner of Ins., 329 Mass. 265, 273-277 (1952). The results were close to those recommended by the Bureau.

c. The drinking age. Effective April 16, 1979, the Legislature raised the legal age for purchasing and selling alcoholic beverages from eighteen to twenty years. St. 1979, c. 15. The Commissioner accepted an analysis by the Division indicating that the lowering of the drinking age in 1973 had increased accident frequencies and that raising the age would have an opposite effect. He found that the Division estimate overstated the effect and should be adjusted to take account, first, of the number of vehicles involved in an accident, and, second, of the difference between lowering the age from twenty-one to eighteen in 1973 and raising it from eighteen to twenty in 1979. But he made an offsetting adjustment because the Division data, counting only accidents where an alcohol-related citation was issued, understated the number of alcohol-related accidents. He made a 1% frequency reduction for all coverages except comprehensive, a result close to that recommended by the Division.

The Bureau attacks the result as optimistic and speculative. It says that in the past the Commissioner has required "compelling evidence" to support a frequency adjustment, citing Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 800 (1976). We agree, as did the Commissioner, that the evidence is not completely satisfactory, particularly with respect to the severity of alcohol-related claims. But we think his conclusion has reasonable support in the evidence. Our conclusion on this point would not be changed if we took into account the Registry statistics and the Probation study included in the plaintiffs' supplementary affidavits.

d. The tort threshold. In many cases an accident victim can recover damages for pain and suffering only if his medical expenses exceed $500. G.L.c. 231, § 6D. This threshold has been steadily eroded by inflation of medical expenses, and the erosion increases claim frequencies for bodily-injury liability. Hence the Commissioner allowed a 1% upward adjustment for this coverage. The Bureau argues that the adjustment is too small. Claims data for 1977 and 1978 would support a larger adjustment, but there was testimony that a reporting problem rendered those data unreliable. We hold that the Commissioner's decision to omit the unreliable data had reasonable support in the evidence.

e. Merit rating. In 1976, the Legislature mandated a merit rating program, imposing surcharges on private passenger vehicles on the basis of accidents and convictions of moving violations of motor vehicle laws. G.L.c. 175, § 113P, inserted by St. 1976, c. 266, § 18. The plan is set forth in 211 Code Mass. Regs. 79.00 (1979). The program could have two possible effects on claim frequencies: a general deterrence effect, inducing policy holders to drive more carefully, and a small claims effect, inducing them not to file claims that might result in a surcharge. The Commissioner accepted the Division's analysis, showing a pattern of correlation between changes in claim frequencies after 1976 and the actual assessment of surcharges. There was a reduction in property-damage claim frequencies from 1976 to 1977, but an increase in bodily-injury frequencies. Causation was blurred by the repeal of the "no-fault" property-damage law and reinstitution of property-damage liability, effective January 1, 1977, by G.L.c. 90, § 340, as appearing in St. 1976, c. 266, § 7, and by the erosion of the tort threshold, discussed above. The Commissioner found that the fact that insurers sent out a flood of merit rating bills late in 1978, coupled with evidence of decreased claim frequencies early in 1979, supported the Division's analysis as a logical explanation of the relative stability from 1977 to 1978. But the Commissioner made an off-setting adjustment for the small claims effect, and applied frequency factors for property-damage and collision coverage about midway between the recommendations of the Bureau and the Division. We think his conclusion had reasonable support in the evidence.

f. 1979 loss experience. Late in the hearings the Bureau presented evidence that paid losses for the first six months of 1979 had increased at a greater rate than the Bureau had predicted in its recommendations. One of the Bureau's supplementary affidavits provided data for nine months of 1979. The Bureau did not revise its recommendations on the basis of this evidence, or otherwise relate this evidence to the rate calculations, but it urges that the evidence lends "impressive support" to its contentions as to inadequacy of the allowance for losses. The Commissioner was not required to supply the missing connections, nor are we. "The Bureau is complaining that in a sense the whole in each case has turned out to be less than the sum of its parts." Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 828 (1976).

5. Allowance for expenses. As in previous years expenses of claim adjustment were treated as part of the allowance for losses. Other expenses were treated separately on the basis of an allowance for each car-year. See Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 808-809 (1976). For 1979 and 1980 the Commissioner started with the allowed expense for the previous year, rather than with actual expense as in the decisions for 1976 and 1978; he then made adjustments based on changed circumstances, "subject to normative scrutiny." The plaintiffs now accept the method and the provisions for commission expense, but they challenge the adjustments to "company expenses" under three headings: the "competition adjustment" factor, costs of merit rating, and expense trends.

a. The "competition adjustment" factor. In his decision for 1979, the Commissioner applied a factor of .95 based on his determination that insurers' expenses should be subjected to downward normative pressure. For 1980 he relied on evidence that there were wide variations among the ratios of company expenses to earned premiums for "agency companies," which sell insurance through independent agents on commission, and that the average ratio for company expense (excluding commissions) for the 65% of the agency companies having the lowest ratios was 85% of the average ratio for all companies. To "avoid too abrupt changes in comparable rate elements from one rate revision to the next," however, he decided to use a factor of .90 rather than .85. Since the 1979 allowance already contained an adjustment factor of .95, this meant that a further factor of .95 was applied to the 1979 allowance.

The Bureau argues that the Commissioner had no authority to adopt such a factor unless he made a finding of "inefficiency" on the part of one or more companies, and that in any event the evidence does not support a factor greater than .95. We disagree on both points. The cases cited by the Bureau do not support a requirement that there be a finding of "inefficiency" on the part of particular companies before "normative" considerations can be introduced into industry-wide ratemaking. See Greenleaf Fin. Co. v. Small Loans Regulatory Bd., 377 Mass. 282, 299-300 (1979), where "the Board found a segment of the industry to be inefficient;" Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 804 (1976) ("regulation should provide cost control as well as cost observation"). Compare New England Tel. Tel. Co. v. Department of Pub. Utils., 360 Mass. 443, 483 (1971) (advertising expenses of utility were allowable in the absence of a showing of "inefficiency or improvidence"); New England Tel. Tel. Co. v. Department of Pub. Utils., 371 Mass. 67, 79-80 (1976) (error to require that charges of parent company be attributed to particular benefits). We agree with the Commissioner's observation in his decision on 1979 rates: "It matters little whether the adjustment is made in the name of countering the exclusion of mutual companies, eliminating the least efficient stock companies, or leveling across state lines." Where a particular item of cost varies widely from company to company and the Commissioner is fixing industry-wide rates, he must be allowed considerable discretion to exclude the highest costs from consideration, even though he cannot prove how they could be reduced.

The evidentiary argument rests on the fact that the Commissioner relied on ratios for "company expenses" (excluding commissions) for the year 1978. According to the Bureau, he should have used ratios for total expenses (including commissions) because some expenses could be transferred from "company expenses" to commissions by giving the agents more responsibility, and he should have used 1976 and 1978 data instead of 1978 data to reduce the effect of temporary fluctuations (eliminating 1977 data because of distortion). Recomputation by the Bureau with these two changes yields a factor of .95 instead of the .90 applied by the Commissioner. We have reviewed the expert testimony on which the Bureau relies, and we find it far less cogent than the Bureau contends. Suffice it that the difference is in matter of fact rather than matter of principle, and the Commissioner's conclusion has reasonable support in the evidence.

b. Costs of merit rating. For 1979 the Commissioner allowed $.50 per property-damage liability policy for the cost of administering the merit rating plan. Reported expenses and projections produced a revised estimate of $2.25 per policy, and the Bureau recommended an additional adjustment of $1.75. The Commissioner, however, accepted the recommendation of the Division, based on extremely wide variation in this item from company to company, that he take into account only the costs of the 65% of the companies with the lowest costs. Accordingly, he approved an additional adjustment of $.65 instead of $1.75. We uphold his decision on the same basis on which we uphold the "competition adjustment" factor, and we see no abuse of discretion in applying that factor to total company expenses, including the adjusted costs of merit rating.

c. Expense trends. The plaintiffs object to the Commissioner's decision on expense trends in two respects: (1) refusal to apply a "supplemental trend factor," and (2) use of a twelve-month trend period instead of the thirteen-month period recommended by the Bureau. We uphold the Commissioner's decision on the "supplemental trend factor" for the reasons stated above with respect to the allowance for losses. See point 4b. The plaintiffs also object to the computation by which the "supplemental trend factor" was eliminated, but the point seems not to have been made to the Commissioner and is not presented to us in such a way that we can evaluate it.

Trends are measured from the average midpoint of one policy year to the average midpoint of the next policy year. By St. 1976, c. 266, § 11, G.L.c. 175, § 113A, was amended to provide for policies issued after January 1. It seems to be agreed that over the succeeding years the average midpoint has shifted from July 1 to August 1, but that no account has been taken of the extra month of inflation. Assuming this to be so, the Commissioner ruled that it did not justify using a thirteen-month period for the trend from 1979 to 1980. We agree.

6. Allowance for profit. In the words of Dr. Fairley, "The financial facts of life — not unrecognized in the industry — are that money is made on investments, not on underwriting." The premiums received are paid out over time for losses and expenses, and the resulting cash flow, together with capital contributed by shareholders, is available for investment. Beginning in 1976 the Commissioner has sought to fix an allowance for underwriting profit which, when added to investment income, would yield a return on shareholder capital comparable to that of unregulated industries of comparable risk. His method is described in Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 813-815 (1976).

In the 1976 decision the Commissioner assumed a hypothetical insurance company which wrote only one line of insurance, began its business at the beginning of the year, and invested available funds in Treasury securities having maturities to fit the cash flow. For property-damage coverages he arrived at a target rate of return on shareholder capital of 10%, a "minimum reasonable investment yield" or "risk-free return" of 6.42% on invested funds, and an allowance for underwriting profit of 5% of premium. For bodily-injury coverages, the allowance for underwriting profit was a negative 4%: "Because of the investment income made possible by the comparatively slow payout of bodily-injury claims, the amount collected in premiums can be 4% less than the amount absorbed by expenses or paid in claims and still provide those who invest in the insurance company with a reasonable return." Id. at 815-816 n. 28. We criticized some of the reasoning as "weakly supported" or as "crude estimation," but we upheld both allowances. Id. at 819, 821.

After the 1976 decision Dr. Fairley revised the model so as to impute to insurers the additional investment income they would derive from investing in more risky securities than Treasury securities. He estimated the critical variables as of the end of 1976, when the government bond yield was about 6%, using actual investment practices of sample realworld insurance companies. In his recommendation for 1980 the Attorney General followed Dr. Fairley's revised model and his estimates, but substituted a "risk-free return" on invested funds of 12.95%, based on market quotations for Treasury securities on October 26, 1979. The Commissioner adopted the Attorney General's recommendation.

For property-damage coverages, the Attorney General recommended a target rate of return on shareholder capital of 15%. To the "risk-free return" of 12.95% on invested funds he added 4.4% as added return from more risky investments. Further calculations, adopted by the Commissioner, produce an allowance for underwriting profit of a negative 2% of premiums. For bodily-injury coverages, a separate calculation yielded an allowance of a negative 13%. The target rate of return is not now in issue; nor is the "risk-free return." But the plaintiffs claim error in three respects: rejection of improved cash flow models proposed by the Bureau, error in the risk factor ("beta") for investments, and attribution to insurers of returns on invested funds that they cannot achieve.

a. Cash flow models. The Bureau submitted what it claims were improved models to estimate cash flows available for investment. The Commissioner said that the adoption of a new cash flow "would produce underwriting profit margin allowances very close to that produced by the old cash flow. For this reason, such updating this year is not crucial and hence makes the old cash flow acceptable." The Bureau had represented that the new cash flows "produced lower underwriting profit provisions although the difference is not great." The plaintiffs now claim that the new cash flow produces about $3 million less investment income on all coverages than the old flow, but we think the Commissioner could properly rely on the Bureau's representation.

b. The risk factor. The Bureau submitted a revised estimate of the risk factor ("beta for assets") to be used in computing the higher yields to be expected when assets are invested in riskier common stocks instead of in Treasury securities. The Bureau's estimate was not used, and no explanation was given in the decision. Dr. Fairley, the Attorney General and the Commissioner used an "average market risk-premium" of 8.8%, the average value for the period 1926-1974. They treated common stocks as having a risk factor of one and bonds as having a risk factor of .125; on the basis of a 1976 sample showing insurer portfolios consisting of 44% in stocks and 56% in bonds, they derived a weighted average of .5. In recent years, however, insurers have invested more heavily in bonds, and for 1978 stocks amounted to less than 24% of the average portfolio; hence the same kinds of computations would yield a risk factor of .34 instead of .5.

Dr. Fairley testified that the calculation of the allowance for profit does not depend on this risk factor, although the factor may enter into the estimation of one of the other variables. In the Attorney General's recommendation adopted by the Commissioner, however, the risk factor of .5 is multiplied by the "market risk-premium" of 8.8%, and the resulting 4.4% is added to the "risk-free return" to obtain the "return on assets." The latter figure, 17.35% for property-damage coverages, enters directly into the calculation of the "profit provision" of a negative 2% of premium. If a risk factor of .34 were used instead of .5, the amount to be added to the "risk-free return" would be 3% (.34 X 8.8%) instead of 4.4% for property-damage coverages. It thus appears that the use of an obsolete and erroneous risk factor was material and should be corrected. The plaintiffs contend that the corrections would mean an increase in premiums of 3%, or more than $20 million, since the same error affects bodily-injury coverages.

c. Unrealistic investment yields. For property-damage coverages, the Commissioner, following Dr. Fairley's model, attributed to the insurers 1980 pre-tax rates of return of 17.35% on investments. He assumed an average tax rate of 20%. There is no prospect, say the plaintiffs, of their earning anything approaching such a yield. The Bureau offered evidence that fifteen major companies had achieved an average pre-tax investment yield for the years 1974-1978 of 5.62%. Using actual yields for taxable bonds, tax-exempt bonds, dividends on stock, and other income, and using a fifteen-year average of annual percentage change in the Standard and Poor's Stock Index for capital gains, the Bureau projected a pre-tax yield of 7.1% on investments in 1980, and an average tax rate of 22%.

There was no evidence that the actual results would be significantly different from those projected by the Bureau, and the Commissioner did not make contrary findings. He rejected the use of actual investment yields on the ground that they were irrelevant. Rates for 1980 should be based on "the flow of funds generated exclusively from policy year 1980 transactions," he said, and should not be affected by investment decisions made in prior years.

We agree in part with the Commissioner's analysis. In our 1976 decision we upheld the use of a model abstracted from the real world. 370 Mass. at 822. Real-world insurers invest funds pooled from many States and several policy years, and the effort to separate out the portion attributable to Massachusetts for the 1980 policy year inevitably involves some abstraction and some simplifying assumptions. But the assumptions should not be "fanciful or impossible to match in the real world." Id.

In the 1976 decision, the Commissioner attributed to the insurers only a "minimum" yield (before taxes) on invested funds, based on the yield that would be achieved by a hypothetical insurer that invested solely in Treasury securities. He assumed a tax rate of 48% "corresponding to the investment policy he assumed." Id. at 815 n. 28. The resulting allowance for profit on property-damage coverages was set at 5% of premiums. "By coincidence a 5% allowance has been traditional in property-damage ratemaking." Id. at 816. We upheld the allowance. We now know that the insurers achieved a much higher yield, paid far less in taxes, and received investment income well in excess of what had been attributed to them. It might well have been reasonable to make an upward adjustment in attributed investment income to take account of real-world investment portfolios and actual taxes.

The computations now before us for 1980, however, require leaps of faith beyond the scope of reasonable inference. In the face of a doubling of the yield on Treasury securities since 1976, the carrying forward of an 8.8 "market risk-premium" based on data from long ago needs and lacks evidentiary support. For a short-term investment program, a yield of 21.75% on common stocks would require that dividend yields of some 6% be supplemented by annual capital gains of 15.75%, far in excess of anything justified by evidence or common experience. The assumed average tax rate of 20% appears to be about right for income on an average 1978 portfolio of taxable bonds taxed at 46%, tax-exempt bonds at zero, and dividends on stock at 6.9%, but the use of such an average tax rate makes it impossible to evaluate the model's attribution of a 14% yield to tax-exempt bonds, subject to a 20% tax, when actual yields on tax-exempt bonds for 1978 averaged less than 6%. The Bureau's evidence showed tax-exempt bonds at more than 40% of the average 1978 portfolio. Finally, the use of market quotations for October 26, 1979, without other support, to set the yields on Treasury securities for 1980 seems highly speculative, although the plaintiffs do not now object on this point. We conclude that the Commissioner's allowance for profit lacks the necessary evidentiary support.

The record before us does not enable us to say what the allowance should be, and we must remand the case to the Commissioner. We do not suggest that he should begin again. We would approve a computation following the method used for 1976, using the estimated 12.95% yield on Treasury securities and a 46% tax rate. Moreover, we would approve an upward adjustment based on actual recent portfolios, fairly projected yields, and applicable actual tax rates. If a risk factor is used, it should be computed consistently with the other assumptions made. There may be other alternatives, and other adjustments may be required to maintain the internal consistency of the model.

7. Confiscation. In view of our conclusion that the allowance for profit must be recomputed, we do not pursue the question whether that allowance results in confiscation. We uphold the allowance for losses and the allowance for expenses as determined by the Commissioner.

8. Conclusion. The case is remanded to the single justice. He is to enter a judgment reversing the decision of the Commissioner and directing him to fix and establish 1980 rates after redetermining the allowance for profit in accordance with this opinion.

So ordered.