1084:
774:(CAPM) which is built in the two-coordinates plane ("standard deviation(risk) -- expected (mean) return") relevant for pricing liquid securities traded on deep financial markets, the TAPA discount rate model is built in the "income growth-capital value growth" coordinates plane, thus it is relevant for pricing all types of income-producing assets, such as property, not just the liquid securities.
784:
22:
406:
1740:
variables specific to the benchmark portfolio, therefore represents the dynamic (expected performance) properties of the benchmark, not any of the properties of the subject asset being valued. Such a conceptualization of discount rates in the TAPA context emphasizes the explicit comparative nature of
2454:
TAPA valuation framework is applicable to pricing assets possessing less than perfect liquidity with reference to a selected valuation benchmark for which the discount rates have to be developed, or forecast, by a valuer. In particular, the TAPA approach has found applications for pricing assets to
252:
1744:
The TAPA theory provides original derivations and conditions under which such BPE can be further reduced to most of the known income capitalization formats within the valuation theory, such as the direct income capitalization format (DIC), The Gordon Growth Model, the Inwood and
Hoskald
1079:{\displaystyle {\text{TAPA's Basic Pricing Equation (BPE), with time-variable discount rates: }}PV(0)=NOI\cdot \sum _{k=1}^{n}{\frac {\quad \prod _{i=2}^{k}(1+u_{o}(i))}{\quad \prod _{i=1}^{k}(1+r(i))}}+PV(0){\frac {\quad \prod _{i=1}^{n}(1+v_{o}(i))}{\quad \prod _{i=1}^{n}(1+r(i))}}}
780:
The TAPA theory lists conditions under which the developed dual-rate general asset pricing model reduces to the conventional single-rate
Discounted cash flow (DCF) analyses framework. Such a framework with time-variable discount rates is called the TAPA BPE (Basic Pricing Equation):
2182:- is an imputed measure of dis-proportionality between the economic interests of the buyer and the seller, with the left-hand-side of the Equation reflecting economic interests of the seller, and the Right-hand side—those of the buyer. If the residual value of the subject asset
2446:, called "the discount rate" in the conventional single-rate DCF applications; as mentioned, TAPA's multi-period discount rate evaluation framework summarized in the formula above allows to determine such converged market rates on a valuation benchmark (portfolio) level.
249:. The multi-period discount rate evaluation theory within TAPA, on the other hand, is a portfolio-level theory, in that it applies to an investment aggregate. A general formula for evaluating discount rates/rates of return at a portfolio-level in TAPA looks as follows
1652:
variables is emphasized in TAPA. The former represent the properties of the subject asset being valued, the latter - the properties of a benchmark (a market aggregate or a portfolio) against which the valuation of subject asset is rendered. The discount rate
2007:
2708:
in some applications of TAPA the subject asset can be a part of the benchmark portfolio, giving rise to some interesting circularity properties in the model, and suggesting macro-economic and counter-cyclical valuation applications for TAPA, see:
510:
173:, which is complemented by a deductive-style multi-period discount rate derivation theory, originating as a generalization of the single-period discount rate framework of Burr-Williams, where the single-period discount rate,
150:. In TAPA, this dynamic valuation predicate forms an underlying new basis for justifying DCF analyses distinct, on the one hand, from the specific-individual-investor DCF premise developed by the American Economist
401:{\displaystyle {\text{TAPA formula for evaluating discount rates, for period i, in multi-period time-variant discount rate setting: }}r(i)={\frac {R\prod _{j=1}^{i}(1+u(j))}{\prod _{j=1}^{i-1}(1+v(j))}}+v(i)}
1741:
any income-approach-based valuation, with TAPA making such a linkage to a valuation benchmark employed explicit via the specification of discount rates in the multi-period analysis framework that it offers.
2459:. Additionally, the flexible time-variable nature of discount rates in the TAPA BPE provides a novel framework for exploring the effects of market cycles on the prices of assets embedded in the markets
1550:
sought at the beginning of the projection period. Thus, as can be seen, TAPA's BPE equation of value is a circular equation usually solvable by numeric methods of evaluation. The distinction of
1760:
130:
neither party should be a losing side to the transaction, meaning that the capital of the buyer and the seller bound up in the transaction should be mutually equal at the end of Period
2415:
1606:
1434:
1290:
1650:
742:
169:, implies a distinct accounting for economic interests of both parties to a transaction with an economic asset, the buyer and the seller, it proceeds from developing a
2281:
2079:
2043:
1516:
1367:
1326:
1211:
2344:; this principle is needed to reduce the dual-rate pricing model to more conventional-looking DCF analyses and TAPA BPE shown above, along with the assumption that
2213:
2140:
1249:
678:
566:
2504:"The Transactional Asset Pricing Approach (TAPA): applications of a new framework for valuing illiquid income-producing assets in the professional valuation context"
616:
2313:
2245:
1548:
1116:
247:
2444:
1738:
1709:
1680:
1175:
645:
533:
2342:
1460:
1142:
768:
2180:
2160:
2107:
1480:
1387:
698:
586:
215:
195:
148:
128:
2574:
411:
2732:"The Transactional Assets Pricing Approach and Income Capitalization Models in Professional Valuation: Towards a "Quick" Income Capitalization Format"
2670:"The Transactional Assets Pricing Approach and Income Capitalization Models in Professional Valuation: Towards a "Quick" Income Capitalization Format"
2456:
512:
is a portfolio-level current return component (yield) for Period 1 of the selected projection period (it is assumed the portfolio is made up of
1462:
series; while the second term—represents the residual (reversionary) value of the subject asset at the end of the projection/holding period
1745:
capitalization formats. One novel income capitalization format obtainable from the TAPA BPE is known as the "Quick capitalization model"
1436:). The first term in the TAPA BPE formula above stands for the discounted (present) value of subject asset's benefits represented by the
777:
Unlike single-period CAPM, TAPA is an explicit multi-period framework for forecasting market (or specific portfolio) rates of return.
98:), from a transactional perspective relying, in the process, on a formulated dynamic principle of transactional equity-in-exchange.
2455:
the
Equitable/Fair standard of value (valuation basis), which is defined in the International Valuation Standards published by the
2283:, like it is assumed in the TAPA BPE context, then the presented dual-rate pricing equation becomes amenable to solutions for
110:
for buyers and sellers in an asset transaction, the essence of which is that by the end of the analysis projection period
2831:
2816:
1177:-is the time-variable discount rate determined under the TAPA multi-period discount rate forecasting framework above;
771:
1753:
Dual-rate asset pricing model developed under TAPA represents a substantial contribution of TAPA to generalizing the
258:
TAPA formula for evaluating discount rates, for period i, in multi-period time-variant discount rate setting:
2731:
2581:
2470:
2417:, i.e. that the buyer's and seller's rates of return converge to some representative market value for such rates,
2826:
2599:
154:
in his Theory of
Interest 1930 book and the perfect-competitive-market-approach to justifying DCF, developed by
2347:
95:
2247:
via an imputation of the asset's own rates of change in capital value expected over the projection period,
2002:{\displaystyle {\text{TAPA dual rate asset pricing model: }}PV(0)\cdot \prod _{i=1}^{n}(1+r^{s}(i))=z\left}
744:
is the expected capital value appreciation rate (growth rate) at the market/portfolio level during periods
83:
51:
94:(DCF) analysis and the resulting income capitalization techniques, such as the Gordon growth formula (see
87:
2109:, respectively, for the purposes of subject asset transactional pricing (hence, the "dual-rate" model);
2623:"The transactional asset pricing approach: Its general framework and applications for property markets"
2471:"The transactional asset pricing approach: Its general framework and applications for property markets"
1553:
2142:- is the expected residual (reversionary) value of the subject asset at the end of its holding period
1754:
91:
2560:
165:
Since the
Transactional approach to asset valuation, whose genesis can be traced back to Book V of
71:
32:
2792:
2713:"транзакционный подход ценообразования (tapa) как инструмент анализа фундаментальных стоимостей?"
2691:
2650:
166:
1757:
analysis framework. The
General pricing equation for this model is as follows:
1392:
1254:
1611:
703:
2784:
2642:
2511:
2490:
2250:
2048:
2012:
1485:
1331:
1295:
1180:
159:
2185:
2112:
1216:
650:
538:
2821:
2776:
2743:
2681:
2634:
2482:
591:
2715:[transactional pricing approach (tapa) as a tool for fundamental value analysis?].
2286:
2218:
1521:
1089:
220:
2420:
1714:
1685:
1656:
1151:
1145:
621:
515:
2321:
1439:
1121:
747:
2539:"Еще раз о ставке дисконтирования в оценочной деятельности и методах ДОХОДНОГО подхода"
2165:
2145:
2092:
1465:
1372:
683:
571:
200:
180:
133:
113:
2600:"Determination of the Fair value of object in sales, donation and barter transactions"
2810:
2796:
2654:
505:{\displaystyle R={\frac {\quad \sum _{s=1}^{n}NOI_{s}}{\quad \sum _{s=1}^{n}PV_{s}}}}
155:
151:
79:
2695:
2503:
1328:-is the expected rate of change in the net operating income from the subject asset
2764:
2541:[Encore on discount rates in appraisal and the income approach methods]
2538:
1118:
stands for the market value of the asset being valued as at the valuation date (
2712:
82:
theory developed in 2000s by a collaboration of
Russian and Israeli economists
2638:
2486:
2788:
2780:
2646:
2515:
2494:
2081:
stand for the expected rates-of-return/discount rates utilized by the buyer (
790:
TAPA's Basic
Pricing Equation (BPE), with time-variable discount rates:
2748:
2686:
2669:
2622:
41:
21:
647:- is the expected rate of change in the aggregate net operating incomes
106:
TAPA approach originates with the framing of the dynamic inter-temporal
2215:
can be assumed to be proportioned to the asset's initial value sought
162:
in their seminal
Dividend policy and growth Paper, on the other hand.
2318:
The dynamic principle of equity-in-exchange mentioned above implies
177:, is conceptualized as being constituted of the current income
2765:"Fair value in the professional valuation: concept and models"
15:
2763:
Artemenkov, Andrey I.; Lodh, Suman; Nandy, Monomita (2018).
1251:
of the asset being valued (subject asset) over the period
170:
2668:
Michaletz, Vladimir B.; Artemenkov, Andrey (2018-03-01).
2621:
Michaletz, Vladimir; Artemenkov, Andrey I. (2019-01-01).
680:
of the assets making up the portfolio during the period
217:
component for a single asset or a portfolio aggregate:
46:
36:
2575:"Dividend Policy, Growth, and the Valuation of Shares"
1213:- is the expected rate of change in the capital value
2423:
2350:
2324:
2289:
2253:
2221:
2188:
2168:
2148:
2115:
2095:
2051:
2015:
1763:
1717:
1688:
1659:
1614:
1556:
1524:
1488:
1468:
1442:
1395:
1375:
1334:
1298:
1257:
1219:
1183:
1154:
1124:
1092:
787:
750:
706:
686:
653:
624:
594:
574:
541:
518:
414:
255:
223:
203:
183:
136:
116:
700:(subsequent to Period 1 ) ; in a similar vein,
2730:Michaletz, Vladimir B.; Artemenkov, Andrey (2018).
2502:Michaletz V.; Artemenkov I.; Medevedeva O. (2019).
2438:
2409:
2336:
2307:
2275:
2239:
2207:
2174:
2154:
2134:
2101:
2073:
2037:
2001:
1732:
1703:
1674:
1644:
1600:
1542:
1510:
1474:
1454:
1428:
1381:
1361:
1320:
1284:
1243:
1205:
1169:
1136:
1110:
1078:
762:
736:
692:
672:
639:
610:
580:
560:
527:
504:
400:
241:
209:
189:
142:
122:
2549:(in Russian) (1). Russian Society of Appraisers.
568:by the end of Analysis Period 1 over the asset
2605:(in Russian). Dnepro: Art Press. p. 278.
197:component and the capital value appreciation
108:principle of transactional equity-in-exchange
90:. It provides a basis for reconstructing the
8:
2769:International Journal of Critical Accounting
2627:Journal of Property Investment & Finance
2475:Journal of Property Investment & Finance
2616:
2614:
2612:
535:assets, each yielding net operating income
2747:
2685:
2457:International Valuation Standards Council
2422:
2377:
2355:
2349:
2323:
2288:
2258:
2252:
2220:
2193:
2187:
2167:
2147:
2120:
2114:
2094:
2056:
2050:
2020:
2014:
1982:
1969:
1937:
1918:
1901:
1888:
1877:
1865:
1854:
1821:
1802:
1791:
1766:TAPA dual rate asset pricing model:
1764:
1762:
1716:
1687:
1658:
1613:
1583:
1561:
1555:
1523:
1493:
1487:
1467:
1441:
1394:
1374:
1333:
1303:
1297:
1256:
1218:
1188:
1182:
1153:
1123:
1091:
1043:
1032:
1007:
988:
977:
969:
918:
907:
882:
863:
852:
844:
838:
827:
788:
786:
749:
705:
685:
664:
652:
623:
602:
593:
573:
552:
540:
517:
493:
480:
469:
456:
440:
429:
421:
413:
344:
333:
297:
286:
276:
256:
254:
222:
202:
182:
135:
115:
2469:Michaletz, V.; Artemenkov, A.I. (2019).
2529:
2410:{\displaystyle r^{b}(i)=r^{s}(i)=r(i)}
1482:, proportioned, via the imputation of
78:(TAPA) is a general reconstruction of
1749:Dual-rate asset pricing model in TAPA
7:
2736:Real Estate Management and Valuation
2674:Real Estate Management and Valuation
1518:terms, to the asset's present value
76:Transactional Asset Pricing Approach
74:theory department of economics, the
2508:European Journal of Natural History
2580:. Chicago Journals. Archived from
14:
1601:{\displaystyle v_{o}(i),u_{o}(i)}
618:as at the beginning of Period 1);
20:
1027:
972:
902:
847:
464:
424:
2433:
2427:
2404:
2398:
2389:
2383:
2367:
2361:
2302:
2296:
2270:
2264:
2234:
2228:
2068:
2062:
2032:
2026:
1952:
1949:
1943:
1924:
1836:
1833:
1827:
1808:
1781:
1775:
1727:
1721:
1698:
1692:
1669:
1663:
1639:
1633:
1624:
1618:
1595:
1589:
1573:
1567:
1537:
1531:
1505:
1499:
1423:
1417:
1356:
1344:
1315:
1309:
1279:
1264:
1238:
1226:
1200:
1194:
1164:
1158:
1105:
1099:
1070:
1067:
1061:
1049:
1022:
1019:
1013:
994:
966:
960:
945:
942:
936:
924:
897:
894:
888:
869:
805:
799:
731:
725:
716:
710:
634:
628:
395:
389:
377:
374:
368:
356:
324:
321:
315:
303:
270:
264:
1:
171:dual rate asset pricing model
2561:"Online Library of Liberty"
2315:e.g. by numerical methods.
2089:) with reference to Period
772:Capital asset pricing model
770:, respectively. Unlike the
2848:
1429:{\displaystyle NOI=NOI(1)}
1285:{\displaystyle i,(i=1..n)}
2639:10.1108/JPIF-10-2018-0078
2487:10.1108/JPIF-10-2018-0078
1645:{\displaystyle v(i),u(i)}
737:{\displaystyle v(i),v(j)}
2781:10.1504/IJCA.2018.098262
2547:Voprosi Ocenki Quarterly
2537:V. B. Michaletz (2005).
2276:{\displaystyle v_{o}(i)}
2074:{\displaystyle r^{s}(i)}
2038:{\displaystyle r^{b}(i)}
1511:{\displaystyle v_{O}(i)}
1362:{\displaystyle NOI(i-1)}
1321:{\displaystyle u_{o}(i)}
1206:{\displaystyle v_{0}(i)}
1144:) determined under the
2749:10.2478/remav-2018-0008
2687:10.2478/remav-2018-0008
2208:{\displaystyle S_{res}}
2135:{\displaystyle S_{res}}
1244:{\displaystyle PV(i-1)}
673:{\displaystyle NOI_{s}}
561:{\displaystyle NOI_{s}}
96:dividend discount model
35:, as no other articles
2598:V.V. Galasyuk (2016).
2440:
2411:
2338:
2309:
2277:
2241:
2209:
2176:
2156:
2136:
2103:
2075:
2039:
2003:
1923:
1876:
1807:
1734:
1705:
1676:
1646:
1602:
1544:
1512:
1476:
1456:
1430:
1383:
1363:
1322:
1286:
1245:
1207:
1171:
1138:
1112:
1080:
1048:
993:
923:
868:
843:
764:
738:
694:
674:
641:
612:
611:{\displaystyle PV_{s}}
582:
562:
529:
506:
485:
445:
402:
355:
302:
243:
211:
191:
144:
124:
2711:Маградзе А.Г (2019).
2441:
2412:
2339:
2310:
2308:{\displaystyle PV(0)}
2278:
2242:
2240:{\displaystyle PV(0)}
2210:
2177:
2157:
2137:
2104:
2076:
2040:
2009:where, additionally,
2004:
1897:
1850:
1787:
1735:
1706:
1677:
1647:
1603:
1545:
1543:{\displaystyle PV(0)}
1513:
1477:
1457:
1431:
1384:
1364:
1323:
1287:
1246:
1208:
1172:
1139:
1113:
1111:{\displaystyle PV(0)}
1081:
1028:
973:
903:
848:
823:
765:
739:
695:
675:
642:
613:
583:
563:
530:
507:
465:
425:
403:
329:
282:
244:
242:{\displaystyle r=R+v}
212:
192:
145:
125:
84:Vladimir B. Michaletz
2439:{\displaystyle r(i)}
2421:
2348:
2322:
2287:
2251:
2219:
2186:
2166:
2146:
2113:
2093:
2049:
2013:
1761:
1755:Discounted cash flow
1733:{\displaystyle u(i)}
1715:
1704:{\displaystyle v(i)}
1686:
1675:{\displaystyle r(i)}
1657:
1612:
1554:
1522:
1486:
1466:
1440:
1393:
1373:
1332:
1296:
1255:
1217:
1181:
1170:{\displaystyle r(i)}
1152:
1122:
1090:
785:
748:
704:
684:
651:
640:{\displaystyle u(j)}
622:
592:
572:
539:
528:{\displaystyle 1..s}
516:
412:
253:
221:
201:
181:
134:
114:
92:discounted cash flow
88:Andrey I. Artemenkov
2832:2000s introductions
2817:Valuation (finance)
2337:{\displaystyle z=1}
1455:{\displaystyle NOI}
1137:{\displaystyle t=0}
763:{\displaystyle i,j}
2436:
2407:
2334:
2305:
2273:
2237:
2205:
2172:
2152:
2132:
2099:
2071:
2035:
1999:
1730:
1701:
1672:
1642:
1598:
1540:
1508:
1472:
1452:
1426:
1379:
1359:
1318:
1282:
1241:
1203:
1167:
1134:
1108:
1076:
760:
734:
690:
670:
637:
608:
578:
558:
525:
502:
398:
239:
207:
187:
167:Nicomachean Ethics
140:
120:
54:for suggestions.
44:to this page from
2175:{\displaystyle z}
2155:{\displaystyle n}
2102:{\displaystyle i}
1767:
1682:, being based on
1475:{\displaystyle n}
1382:{\displaystyle i}
1074:
949:
791:
693:{\displaystyle j}
581:{\displaystyle s}
500:
381:
259:
210:{\displaystyle v}
190:{\displaystyle R}
160:Franco Modigliani
143:{\displaystyle n}
123:{\displaystyle n}
68:
67:
2839:
2827:Financial models
2801:
2800:
2760:
2754:
2753:
2751:
2727:
2721:
2720:
2706:
2700:
2699:
2689:
2665:
2659:
2658:
2618:
2607:
2606:
2604:
2595:
2589:
2588:
2586:
2579:
2571:
2565:
2564:
2557:
2551:
2550:
2544:
2534:
2519:
2498:
2445:
2443:
2442:
2437:
2416:
2414:
2413:
2408:
2382:
2381:
2360:
2359:
2343:
2341:
2340:
2335:
2314:
2312:
2311:
2306:
2282:
2280:
2279:
2274:
2263:
2262:
2246:
2244:
2243:
2238:
2214:
2212:
2211:
2206:
2204:
2203:
2181:
2179:
2178:
2173:
2161:
2159:
2158:
2153:
2141:
2139:
2138:
2133:
2131:
2130:
2108:
2106:
2105:
2100:
2080:
2078:
2077:
2072:
2061:
2060:
2044:
2042:
2041:
2036:
2025:
2024:
2008:
2006:
2005:
2000:
1998:
1994:
1993:
1992:
1974:
1973:
1955:
1942:
1941:
1922:
1917:
1893:
1892:
1875:
1864:
1826:
1825:
1806:
1801:
1768:
1765:
1739:
1737:
1736:
1731:
1710:
1708:
1707:
1702:
1681:
1679:
1678:
1673:
1651:
1649:
1648:
1643:
1607:
1605:
1604:
1599:
1588:
1587:
1566:
1565:
1549:
1547:
1546:
1541:
1517:
1515:
1514:
1509:
1498:
1497:
1481:
1479:
1478:
1473:
1461:
1459:
1458:
1453:
1435:
1433:
1432:
1427:
1388:
1386:
1385:
1380:
1368:
1366:
1365:
1360:
1327:
1325:
1324:
1319:
1308:
1307:
1291:
1289:
1288:
1283:
1250:
1248:
1247:
1242:
1212:
1210:
1209:
1204:
1193:
1192:
1176:
1174:
1173:
1168:
1143:
1141:
1140:
1135:
1117:
1115:
1114:
1109:
1085:
1083:
1082:
1077:
1075:
1073:
1047:
1042:
1025:
1012:
1011:
992:
987:
970:
950:
948:
922:
917:
900:
887:
886:
867:
862:
845:
842:
837:
792:
789:
769:
767:
766:
761:
743:
741:
740:
735:
699:
697:
696:
691:
679:
677:
676:
671:
669:
668:
646:
644:
643:
638:
617:
615:
614:
609:
607:
606:
587:
585:
584:
579:
567:
565:
564:
559:
557:
556:
534:
532:
531:
526:
511:
509:
508:
503:
501:
499:
498:
497:
484:
479:
462:
461:
460:
444:
439:
422:
407:
405:
404:
399:
382:
380:
354:
343:
327:
301:
296:
277:
260:
257:
248:
246:
245:
240:
216:
214:
213:
208:
196:
194:
193:
188:
149:
147:
146:
141:
129:
127:
126:
121:
102:General overview
63:
60:
49:
47:related articles
24:
16:
2847:
2846:
2842:
2841:
2840:
2838:
2837:
2836:
2807:
2806:
2805:
2804:
2762:
2761:
2757:
2729:
2728:
2724:
2710:
2707:
2703:
2667:
2666:
2662:
2620:
2619:
2610:
2602:
2597:
2596:
2592:
2584:
2577:
2573:
2572:
2568:
2559:
2558:
2554:
2542:
2536:
2535:
2531:
2526:
2501:
2468:
2465:
2463:Further reading
2452:
2419:
2418:
2373:
2351:
2346:
2345:
2320:
2319:
2285:
2284:
2254:
2249:
2248:
2217:
2216:
2189:
2184:
2183:
2164:
2163:
2144:
2143:
2116:
2111:
2110:
2091:
2090:
2052:
2047:
2046:
2016:
2011:
2010:
1978:
1965:
1933:
1884:
1849:
1845:
1817:
1759:
1758:
1751:
1713:
1712:
1684:
1683:
1655:
1654:
1610:
1609:
1579:
1557:
1552:
1551:
1520:
1519:
1489:
1484:
1483:
1464:
1463:
1438:
1437:
1391:
1390:
1371:
1370:
1330:
1329:
1299:
1294:
1293:
1253:
1252:
1215:
1214:
1184:
1179:
1178:
1150:
1149:
1146:Income approach
1120:
1119:
1088:
1087:
1026:
1003:
971:
901:
878:
846:
783:
782:
746:
745:
702:
701:
682:
681:
660:
649:
648:
620:
619:
598:
590:
589:
570:
569:
548:
537:
536:
514:
513:
489:
463:
452:
423:
410:
409:
328:
278:
251:
250:
219:
218:
199:
198:
179:
178:
132:
131:
112:
111:
104:
64:
58:
55:
45:
42:introduce links
25:
12:
11:
5:
2845:
2843:
2835:
2834:
2829:
2824:
2819:
2809:
2808:
2803:
2802:
2755:
2722:
2717:Voproci Ocenki
2701:
2660:
2633:(3): 255–288.
2608:
2590:
2587:on 2018-10-11.
2566:
2552:
2528:
2527:
2525:
2522:
2521:
2520:
2499:
2481:(3): 255–288.
2464:
2461:
2451:
2448:
2435:
2432:
2429:
2426:
2406:
2403:
2400:
2397:
2394:
2391:
2388:
2385:
2380:
2376:
2372:
2369:
2366:
2363:
2358:
2354:
2333:
2330:
2327:
2304:
2301:
2298:
2295:
2292:
2272:
2269:
2266:
2261:
2257:
2236:
2233:
2230:
2227:
2224:
2202:
2199:
2196:
2192:
2171:
2151:
2129:
2126:
2123:
2119:
2098:
2085:) and seller (
2070:
2067:
2064:
2059:
2055:
2034:
2031:
2028:
2023:
2019:
1997:
1991:
1988:
1985:
1981:
1977:
1972:
1968:
1964:
1961:
1958:
1954:
1951:
1948:
1945:
1940:
1936:
1932:
1929:
1926:
1921:
1916:
1913:
1910:
1907:
1904:
1900:
1896:
1891:
1887:
1883:
1880:
1874:
1871:
1868:
1863:
1860:
1857:
1853:
1848:
1844:
1841:
1838:
1835:
1832:
1829:
1824:
1820:
1816:
1813:
1810:
1805:
1800:
1797:
1794:
1790:
1786:
1783:
1780:
1777:
1774:
1771:
1750:
1747:
1729:
1726:
1723:
1720:
1700:
1697:
1694:
1691:
1671:
1668:
1665:
1662:
1641:
1638:
1635:
1632:
1629:
1626:
1623:
1620:
1617:
1597:
1594:
1591:
1586:
1582:
1578:
1575:
1572:
1569:
1564:
1560:
1539:
1536:
1533:
1530:
1527:
1507:
1504:
1501:
1496:
1492:
1471:
1451:
1448:
1445:
1425:
1422:
1419:
1416:
1413:
1410:
1407:
1404:
1401:
1398:
1378:
1358:
1355:
1352:
1349:
1346:
1343:
1340:
1337:
1317:
1314:
1311:
1306:
1302:
1281:
1278:
1275:
1272:
1269:
1266:
1263:
1260:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1202:
1199:
1196:
1191:
1187:
1166:
1163:
1160:
1157:
1133:
1130:
1127:
1107:
1104:
1101:
1098:
1095:
1072:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1046:
1041:
1038:
1035:
1031:
1024:
1021:
1018:
1015:
1010:
1006:
1002:
999:
996:
991:
986:
983:
980:
976:
968:
965:
962:
959:
956:
953:
947:
944:
941:
938:
935:
932:
929:
926:
921:
916:
913:
910:
906:
899:
896:
893:
890:
885:
881:
877:
874:
871:
866:
861:
858:
855:
851:
841:
836:
833:
830:
826:
822:
819:
816:
813:
810:
807:
804:
801:
798:
795:
759:
756:
753:
733:
730:
727:
724:
721:
718:
715:
712:
709:
689:
667:
663:
659:
656:
636:
633:
630:
627:
605:
601:
597:
588:capital value
577:
555:
551:
547:
544:
524:
521:
496:
492:
488:
483:
478:
475:
472:
468:
459:
455:
451:
448:
443:
438:
435:
432:
428:
420:
417:
397:
394:
391:
388:
385:
379:
376:
373:
370:
367:
364:
361:
358:
353:
350:
347:
342:
339:
336:
332:
326:
323:
320:
317:
314:
311:
308:
305:
300:
295:
292:
289:
285:
281:
275:
272:
269:
266:
263:
238:
235:
232:
229:
226:
206:
186:
139:
119:
103:
100:
66:
65:
52:Find link tool
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
2844:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2814:
2812:
2798:
2794:
2790:
2786:
2782:
2778:
2774:
2770:
2766:
2759:
2756:
2750:
2745:
2741:
2737:
2733:
2726:
2723:
2719:(in Russian).
2718:
2714:
2705:
2702:
2697:
2693:
2688:
2683:
2680:(1): 89–107.
2679:
2675:
2671:
2664:
2661:
2656:
2652:
2648:
2644:
2640:
2636:
2632:
2628:
2624:
2617:
2615:
2613:
2609:
2601:
2594:
2591:
2583:
2576:
2570:
2567:
2562:
2556:
2553:
2548:
2540:
2533:
2530:
2523:
2517:
2513:
2509:
2505:
2500:
2496:
2492:
2488:
2484:
2480:
2476:
2472:
2467:
2466:
2462:
2460:
2458:
2449:
2447:
2430:
2424:
2401:
2395:
2392:
2386:
2378:
2374:
2370:
2364:
2356:
2352:
2331:
2328:
2325:
2316:
2299:
2293:
2290:
2267:
2259:
2255:
2231:
2225:
2222:
2200:
2197:
2194:
2190:
2169:
2149:
2127:
2124:
2121:
2117:
2096:
2088:
2084:
2065:
2057:
2053:
2029:
2021:
2017:
1995:
1989:
1986:
1983:
1979:
1975:
1970:
1966:
1962:
1959:
1956:
1946:
1938:
1934:
1930:
1927:
1919:
1914:
1911:
1908:
1905:
1902:
1898:
1894:
1889:
1885:
1881:
1878:
1872:
1869:
1866:
1861:
1858:
1855:
1851:
1846:
1842:
1839:
1830:
1822:
1818:
1814:
1811:
1803:
1798:
1795:
1792:
1788:
1784:
1778:
1772:
1769:
1756:
1748:
1746:
1742:
1724:
1718:
1695:
1689:
1666:
1660:
1636:
1630:
1627:
1621:
1615:
1592:
1584:
1580:
1576:
1570:
1562:
1558:
1534:
1528:
1525:
1502:
1494:
1490:
1469:
1449:
1446:
1443:
1420:
1414:
1411:
1408:
1405:
1402:
1399:
1396:
1376:
1353:
1350:
1347:
1341:
1338:
1335:
1312:
1304:
1300:
1276:
1273:
1270:
1267:
1261:
1258:
1235:
1232:
1229:
1223:
1220:
1197:
1189:
1185:
1161:
1155:
1147:
1131:
1128:
1125:
1102:
1096:
1093:
1064:
1058:
1055:
1052:
1044:
1039:
1036:
1033:
1029:
1016:
1008:
1004:
1000:
997:
989:
984:
981:
978:
974:
963:
957:
954:
951:
939:
933:
930:
927:
919:
914:
911:
908:
904:
891:
883:
879:
875:
872:
864:
859:
856:
853:
849:
839:
834:
831:
828:
824:
820:
817:
814:
811:
808:
802:
796:
793:
778:
775:
773:
757:
754:
751:
728:
722:
719:
713:
707:
687:
665:
661:
657:
654:
631:
625:
603:
599:
595:
575:
553:
549:
545:
542:
522:
519:
494:
490:
486:
481:
476:
473:
470:
466:
457:
453:
449:
446:
441:
436:
433:
430:
426:
418:
415:
392:
386:
383:
371:
365:
362:
359:
351:
348:
345:
340:
337:
334:
330:
318:
312:
309:
306:
298:
293:
290:
287:
283:
279:
273:
267:
261:
236:
233:
230:
227:
224:
204:
184:
176:
172:
168:
163:
161:
157:
156:Merton Miller
153:
152:Irving Fisher
137:
117:
109:
101:
99:
97:
93:
89:
85:
81:
80:asset pricing
77:
73:
62:
53:
48:
43:
39:
38:
34:
29:This article
27:
23:
18:
17:
2772:
2768:
2758:
2739:
2735:
2725:
2716:
2704:
2677:
2673:
2663:
2630:
2626:
2593:
2582:the original
2569:
2555:
2546:
2532:
2510:(5): 31–36.
2507:
2478:
2474:
2453:
2450:Applications
2317:
2086:
2082:
1752:
1743:
1369:over period
779:
776:
174:
164:
107:
105:
75:
69:
56:
30:
1608:vis-a-vis
2811:Categories
2775:(6): 427.
2742:: 89–107.
2524:References
59:March 2022
50:; try the
37:link to it
2797:217428099
2789:1757-9848
2655:159143650
2647:1463-578X
2516:2073-4972
2495:1463-578X
1899:∏
1895:⋅
1870:−
1852:∑
1789:∏
1785:⋅
1351:−
1233:−
1030:∏
975:∏
905:∏
850:∏
825:∑
821:⋅
467:∑
427:∑
408:, where
349:−
331:∏
284:∏
72:valuation
40:. Please
2696:73613188
2822:Pricing
1086:where,
70:In the
2795:
2787:
2694:
2653:
2645:
2514:
2493:
33:orphan
31:is an
2793:S2CID
2692:S2CID
2651:S2CID
2603:(PDF)
2585:(PDF)
2578:(PDF)
2543:(PDF)
2785:ISSN
2643:ISSN
2512:ISSN
2491:ISSN
2045:and
1711:and
158:and
86:and
2777:doi
2744:doi
2682:doi
2635:doi
2483:doi
1389:. (
1274:1..
520:1..
2813::
2791:.
2783:.
2773:10
2771:.
2767:.
2740:26
2738:.
2734:.
2690:.
2678:26
2676:.
2672:.
2649:.
2641:.
2631:37
2629:.
2625:.
2611:^
2545:.
2506:.
2489:.
2479:37
2477:.
2473:.
2162:;
1292:;
1148:;
2799:.
2779::
2752:.
2746::
2698:.
2684::
2657:.
2637::
2563:.
2518:.
2497:.
2485::
2434:)
2431:i
2428:(
2425:r
2405:)
2402:i
2399:(
2396:r
2393:=
2390:)
2387:i
2384:(
2379:s
2375:r
2371:=
2368:)
2365:i
2362:(
2357:b
2353:r
2332:1
2329:=
2326:z
2303:)
2300:0
2297:(
2294:V
2291:P
2271:)
2268:i
2265:(
2260:o
2256:v
2235:)
2232:0
2229:(
2226:V
2223:P
2201:s
2198:e
2195:r
2191:S
2170:z
2150:n
2128:s
2125:e
2122:r
2118:S
2097:i
2087:s
2083:b
2069:)
2066:i
2063:(
2058:s
2054:r
2033:)
2030:i
2027:(
2022:b
2018:r
1996:]
1990:s
1987:e
1984:r
1980:S
1976:+
1971:n
1967:I
1963:O
1960:N
1957:+
1953:)
1950:)
1947:i
1944:(
1939:b
1935:r
1931:+
1928:1
1925:(
1920:n
1915:1
1912:+
1909:k
1906:=
1903:i
1890:k
1886:I
1882:O
1879:N
1873:1
1867:n
1862:1
1859:=
1856:k
1847:[
1843:z
1840:=
1837:)
1834:)
1831:i
1828:(
1823:s
1819:r
1815:+
1812:1
1809:(
1804:n
1799:1
1796:=
1793:i
1782:)
1779:0
1776:(
1773:V
1770:P
1728:)
1725:i
1722:(
1719:u
1699:)
1696:i
1693:(
1690:v
1670:)
1667:i
1664:(
1661:r
1640:)
1637:i
1634:(
1631:u
1628:,
1625:)
1622:i
1619:(
1616:v
1596:)
1593:i
1590:(
1585:o
1581:u
1577:,
1574:)
1571:i
1568:(
1563:o
1559:v
1538:)
1535:0
1532:(
1529:V
1526:P
1506:)
1503:i
1500:(
1495:O
1491:v
1470:n
1450:I
1447:O
1444:N
1424:)
1421:1
1418:(
1415:I
1412:O
1409:N
1406:=
1403:I
1400:O
1397:N
1377:i
1357:)
1354:1
1348:i
1345:(
1342:I
1339:O
1336:N
1316:)
1313:i
1310:(
1305:o
1301:u
1280:)
1277:n
1271:=
1268:i
1265:(
1262:,
1259:i
1239:)
1236:1
1230:i
1227:(
1224:V
1221:P
1201:)
1198:i
1195:(
1190:0
1186:v
1165:)
1162:i
1159:(
1156:r
1132:0
1129:=
1126:t
1106:)
1103:0
1100:(
1097:V
1094:P
1071:)
1068:)
1065:i
1062:(
1059:r
1056:+
1053:1
1050:(
1045:n
1040:1
1037:=
1034:i
1023:)
1020:)
1017:i
1014:(
1009:o
1005:v
1001:+
998:1
995:(
990:n
985:1
982:=
979:i
967:)
964:0
961:(
958:V
955:P
952:+
946:)
943:)
940:i
937:(
934:r
931:+
928:1
925:(
920:k
915:1
912:=
909:i
898:)
895:)
892:i
889:(
884:o
880:u
876:+
873:1
870:(
865:k
860:2
857:=
854:i
840:n
835:1
832:=
829:k
818:I
815:O
812:N
809:=
806:)
803:0
800:(
797:V
794:P
758:j
755:,
752:i
732:)
729:j
726:(
723:v
720:,
717:)
714:i
711:(
708:v
688:j
666:s
662:I
658:O
655:N
635:)
632:j
629:(
626:u
604:s
600:V
596:P
576:s
554:s
550:I
546:O
543:N
523:s
495:s
491:V
487:P
482:n
477:1
474:=
471:s
458:s
454:I
450:O
447:N
442:n
437:1
434:=
431:s
419:=
416:R
396:)
393:i
390:(
387:v
384:+
378:)
375:)
372:j
369:(
366:v
363:+
360:1
357:(
352:1
346:i
341:1
338:=
335:j
325:)
322:)
319:j
316:(
313:u
310:+
307:1
304:(
299:i
294:1
291:=
288:j
280:R
274:=
271:)
268:i
265:(
262:r
237:v
234:+
231:R
228:=
225:r
205:v
185:R
175:r
138:n
118:n
61:)
57:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
