Managing Snow Risks: The Case of City Governments and Ski Resorts

Transcription

1 Managng Snow Rsks: The Case of Cty Governments and Sk Resorts Haruyosh Ito* Assstant Professor of Fnance Graduate School of Internatonal Management Internatonal Unversty of Japan 777 Kokusacho, Mnam Uonuma-sh Ngata , Japan Tel: * ndcates correspondng author 1

2 Managng Snow Rsks: The Case of Cty Governments and Sk Resorts 1 Introducton Ths paper proposes the rsk management methods usng Snow Dervatves for local cty governments and sk resorts. We defne snow dervatves as the weather dervatves whose underlyng asset s ndex related to snowfall. Frst of all, ths paper studes the mpact of snowfall on the fnancal performance of sk resorts and the local cty government. Our prelmnary analyss shows that the revenues of the sk resorts and snowfall are n quadratc form (nverted U-shaped) whle the snowfall has sgnfcant adverse mpact on the revenues of the cty government. We then desgn the snow dervatves n order to hedge the rsks assocated wth snowfall and examne the contrbutons of proposed dervatves to the corporate value of the sk resorts and the local cty government. In partcular, we use Wang Transform model to ncorporate the managers rsk preference n the evaluaton of snow dervatves. We would expect to show that our proposed snow dervatves contrbute the value of sk resorts and the local cty government. Ths paper also contrbutes to the lterature provdng the comprehensve analyss of weather rsk management. We would expect ths paper encouragng the use of snow dervatves for both sk resorts and local governments as few of them utlze the dervatves for snow rsk management accordng to Bank and Wesner (2011) whch concludes that the reason why the weather dervatves are not frequently used n Australan markets s the lack of understandng to the weather dervatves. 2 Impact of Snowfall on Vstors for Sk Resorts Frst of all, we estmate the mpact of snowfall on fnancal performance of sk resorts. We use maxmum snow depth as varable assocated wth snowfall n our prelmnary analyss. We select three representatve sk resorts n Ngata prefecture whch s one of the most popular sk areas n Japan. We use OLS to estmate the mpact of snowfall on the number of vstors. 2.1 Data We retreve the weather data from Japan Meteorology Agency ( We choose the Yuzawa as a weather observatory snce ths s the closest to these sk resorts. Data s retreved from 1992 to 2012 but 2002 due to the mssng data by 2

3 Yuzawa observatory. We also retreve the data of number of vstors to the sk resorts from several sources such as the whte papers and publcly avalable nformaton such as Lst of Number of Vstors for each Sk Resort n each Year ( as well as prvate nformaton provded by Mnamuonuma Toursm Assocaton (Mnamuonuma Kanko Kyoka n Japanese). We ntally pck up three sk resorts Joetsu Internatonal Sk Resort (Joetsu Kokusa), Gala Sk Resort, and Iwappara Sk Resort snce they have relatvely large number of vstors and ther numbers of vstors are suffcently avalable for our analyss. 2.2 Regresson Analyss We analyze the mpact of snowfall on the number of vstors usng regresson analyss. uadratc form s employed snce lnear form s not approprate due to the untabulated analyss. The functonal form we specfy s 2 y, t a bxt c xt, t (1) Where y,t s number of vstors of the sk resort n season t, x t s maxmum snow depth observed n season t n Yuzawa. 2.3 Prelmnary Results Regresson results are shown n Table 1. Table 1 Snowfall Effects on the Number of Vstors (Unt: 10,000) Joetsu Internatonal Gala Iwappara Intercept (20.72) (9.43) (47.82) Maxmum Snow Depth (m) *** ** * (19.24) (8.76) (44.40) Maxmum Snow Depth *** ** * (4.31) (1.96) (9.93) Adj R N Note: ***, **, and * ndcate 1%, 5%, and 10% level of sgnfcance. Standard devaton s n parenthess. Adj. R 2 ndcates adjusted coeffcent of determnaton, and N ndcates number of sample. 3

4 Regresson analyss shows that there s an optmal snow depth for each sk resort snce the relatonshp between snow depth and number of vstors s specfed by quadratc form. Coeffcents to the square term are sgnfcant for all sk resorts. 3 Impact of Snowfall on Snow Removal Costs We then analyze the mpact of snowfall on the snow removal cost mposed to local cty government. We use the fnancal data provded by the Uonuma cty, whch s close to the sk resorts analyzed n the prevous chapter. 3.1 Regresson Analyss The equaton specfed n ths analyss s gven by c a (2) t bx t t where c t s cost of snow removal for Uonuma cty n year t, x t s maxmum snow depth observed n season t n Yuzawa. We estmate these coeffcents by generalzed least square method snce the we detect seral correlaton n the prelmnary analyss. 3.2 Regresson Results Regresson results are shown n Table 2 Table 2: Impact of Maxmum Snow Depth on Snow Removal Cost for Uonuma Cty Uonuma Cty Intercept 265,753 (146,656) Maxmum Snow Depth (m) 195,241 *** (33,101) AIC BIC N 9 Note: *** ndcates 1% level of sgnfcance. Standard devaton s n parenthess. AIC and BIC ndcate Akake Informaton Crtera and Bayesan Informaton Crtera respectvely. 4 Smulaton Analyss and Value of Dervatves for Sk Resorts and Local Cty We run the smulaton analyss to generate the cash flows for sk resorts and local cty government. 4

5 4.1 Net Cash Flow for Sk Resorts NCFSR n ~ vstor sales per customer cost ~ ~ ~ 4.50 S S n vstor where NCF SR ndcates Net Cash Flow for sk resorts n vstor ndcates number of vstors to the sk resorts. We assume that sales per customer are 3,000 JPY (250 USD), and cost ndcates the cost to the sk resorts. We assume ths s fx costs and amounts 140 mllon JPY (1.7 thousand USD). S ndcates maxmum snow depth, whch s estmated by smulaton. We assume S follows normal dstrbuton wth mean = meter and standard devaton = meter. Assumpton of normal dstrbuton s rejected by nether Jack-Bella test nor Kolmogorov-Smrnov test. 4.2 Net Cash Flow for the Local Cty Government NCF Cty net revenue c~ snowremovalcost ~ c ~ 195,241 S 265,753 snow removalcost where NCF Cty ndcates Net Cash Flow for local cty government, net revenue s the revenue mnus the cost other than snow removal cost. We assume net revenue s fxed and ndependent wth snow depth. c snowremovalcost ndcates snow removal cost for the local cty government. 4.3 Smulaton Results Smulaton results are summarzed n Table 3. As Table 3 shows, the mpact of snowfall on the sk resort s sgnfcant as the sk resort cash flow can be negatve dependng on the amount of snow depth. Table 3: Summary Statstcs of Smulaton Results Sk Resort Cty Offce Cash Flow No Dervatves Cash Flow No Dervatves Mean 255,616 2,309,264 Medan 293,171 2,308,983 Standard Devaton 95, ,586 Max 321,884 2,810,189 Mn (655,895) 1,827,356 Skewness

6 5 Value of the Snow Dervatves Based on the smulaton and regresson results, we desgn the snow dervatves for the sk resort and the cty government. Then we evaluate the value of snow dervatves for these enttes. 5.1 Mechansm of Snow Dervatves For the Sk Resort the payoff of the weather dervatve s gven by Max [1,940,000 JPY (2.3 - S), 0], where S s maxmum snow depth measured n meter. 1,940,000 JPY s same as 16,167 USD. Accordng to the regresson results, the revenue would be maxmzed f snow depth s 2.3 m. Thus, the payoff s same as long poston n put opton. We assume the cty offce would be the seller of ths put opton. The payoff to the cty government s - Max [1,940,000 JPY (2.3 - S), 0]. 5.2 Overvew of the Wang Transform We employ Wang Transform (Wang 2002) for the valuaton of proposed snow dervatves snce underlyng assets of the snow dervatve s maxmum snow depth whch s not traded n the markets. We need the valuaton method under ncompleteness. Wang Transform s gven by F x 1 F P x where, F (x) s cumulatve dstrbuton functon under rsk-neutral measure,, ( ) ndcates cumulatve dstrbuton functon of standard normal dstrbuton, Φ -1 ( ) s nverse functon of Φ( ), F P (x) s cumulatve dstrbuton functon under physcal probablty measure, P, λ s the coeffcent of rsk averson. If the coeffcent s postve, dstrbuton functon s shfted to left. The subjectve probablty for bad scenaro (lower revenue) s hgher and that for good scenaro (hgher revenue) s lower. The ssue when employng Wang Transforms s estmaton of λ. Ito, A, and Ozawa (2014) employ survey method to estmate the λ dstrbutng the questonnare to the mangers of J. League, premer soccer league n Japan. Ther estmaton results show that most probable ranges of lambda s from 0.25 to We employ the senstvty analyss for the valuaton analyss of weather dervatves dependng on the λ and the premum to the weather dervatves. 5.3 Valuaton Analyss of Snow Dervatves V We evaluate the value of snow dervatves for the team by NCF E NCF E wth_ hedge wthout_ hedge. where, (3) 6

7 E f E I NCFwthouthedge NCFwthout _ hedge, f NCFwthout _ hedge, 1 NCF F NCF F NCF wthout_ hedge, wthout_ hedge, wthout_ hedge, 1 I NCFwthhedge NCFwth_ hedge, f NCFwth_ hedge, 1 NCF F NCF F NCF f wth _ hedge, wth _ hedge, wth _ hedge, 1. Where ndcates th smallest NCF among the smulaton paths. NCF wth_hedge s equal to NCF wthout_hedge + payoff from the snow dervatves mnus the premum of weather dervatves. Table 4 and 5 summarze the value of the snow dervatves for the sk resort and the cty government dependng on the premum of weather dervatves and λ. Table 4: Value of Proposed Weather Dervatves for Sk Resort by Wang Transform (n thousand JPY) Value of Hedgng Instrument λ 0% 5% 10% 15% 20% 60% 0 0 (3,291) (6,583) (9,874) (13,166) (39,497) 0.1 1,318 (1,973) (5,265) (8,556) (11,847) (38,179) 0.2 2,889 (402) (3,694) (6,985) (10,277) (36,608) , (2,811) (6,103) (9,394) (35,726) 0.3 4,720 1,428 (1,863) (5,155) (8,446) (34,777) 0.4 6,815 3, (3,059) (6,350) (32,682) 0.5 9,177 5,886 2,594 (697) (3,988) (30,320) ,682 6,390 3,099 (193) (3,484) (29,816) ,805 8,513 5,222 1,930 (1,361) (27,693) ,693 11,401 8,110 4,818 1,527 (24,805) ,834 14,543 11,252 7,960 4,669 (21,663) ,220 17,929 14,637 11,346 8,055 (18,277) 1 24,838 21,546 18,255 14,964 11,672 (14,659) Note: Second column ndcate the safety loadng. 5% mples premum of the snow dervatves s 1.05 tmes E [Max (1,940,000 JPY (2.3 - S),0)] = ,820 = 69,111. Bold value ndcate the most probable range of λ by Ito, A, and Ozawa (2014). 7

8 Table 5: Value of Proposed Weather Dervatves for Sk Resort by Wang Transform (n thousand JPY) Value of Hedgng Instrument λ 0% 5% 10% 15% 20% 60% 0 0 3,292 6,583 9,875 13,166 39, ,382 10,674 13,965 17,257 20,548 46, ,221 17,513 20,804 24,095 27,387 53, ,437 20,728 24,020 27,311 30,603 56, ,519 23,810 27,101 30,393 33,684 60, ,279 29,571 32,862 36,154 39,445 65, ,515 34,807 38,098 41,389 44,681 71, ,501 35,792 39,084 42,375 45,667 71, ,242 39,533 42,824 46,116 49,407 75, ,478 43,770 47,061 50,353 53,644 79, ,249 47,540 50,831 54,123 57,414 83, ,580 50,872 54,163 57,455 60,746 87, ,502 53,793 57,085 60,376 63,668 89,999 Note: Second column ndcate the safety loadng. 5% mples premum of the snow dervatves s 1.05 tmes E [Max (1,940,000 JPY (2.3 - S),0)] = ,820 = 69,111. Bold value ndcate the most probable range of λ by Ito, A, and Ozawa (2014). Table 4 shows that the snow dervatves would contrbute to mprovement of the corporate value f the prce of weather dervatves s reasonably low and managers rsk averson s relatvely hgh. Table 5 also shows that n any case, ths type of dervatves would contrbute to the value of cty government. Thus low premum tradng would be possble f the cty government s the underwrter of ths contracts. 6 Summary and Future Study We prelmnary analyze the mpact of snow depth on the fnancal performance of snow resort and local cty government. We would lke to refne the model by pursung the better defnton of snowfall such as usng the number of snow days settng up several thresholds n regard to snowfall. Also we would lke to ntroduce the control varables such as macroeconomc factors n order to assure our analyss s robust. We also plan to apply maxmum value theorem n order to model the dstrbuton of maxmum snow depth. Whle we would not reject the normal dstrbuton assumpton on the dstrbuton, generalzed extreme value dstrbutons mght ft better to the hstorcal dstrbuton of snow depth than normal dstrbuton. We also plan to estmate the rsk averson of managers n order to make our model more practcal to mplement rsk management for sk resorts and local governments. 8

9 Reference [1] Bank, M. And Wesner R. (2011). Determnants of Weather Dervatves Usage n the Austraran Wnter Toursm Industry. Toursm Managmeent, 32, [2] Ito, H., A, J., and Ozawa, A. (2014). Managng Weather Rsks: The Case of J. League Soccer Teams n Japan. Journal of Rsk and Insurance, forthcomng. [3] Wang, Shaun S., 2002, A Unversal Framework for Prcng Fnancal and Insurance Rsks, ASTIN Bulletn, 32(2),