The Excel file Dataset for Real Estate contains the median monthly household income by household size and the property price per square meter for Class A and Class B residential properties in Kowloon for the annual period from 2011 to 2019

Consider the median monthly household income for a typical household with THREE economically active members. Suppose the household can only commit up to 1/3 of its income to mortgage payment. The usual mortgage terms are 20-year, monthly payments, with mortgage rate equal to Prime Rate (5%) minus 2.5%, and 30% down payment. Assume that the household has enough savings to make the 30% down payment for property price.

(a) Determine the maximum home price the household can afford each year from 2011 to 2019? Hint: Based on the median household income and the mortgage terms, the maximum mortgage an average household can borrow is determined as follows: = [ 1 (1 + /12)12 /12 ] Where r is the annual mortgage rate, n is the mortgage term (20 years) and PMT is the monthly mortgage payment?

(b) Suppose the 3-member household wishes to buy and own a class B property in Kowloon of size 60 square meters. Plot the time series of the affordable home prices calculated in (a) and the corresponding class B property prices for the period from 2011 to 2010.

(c) Following our discussion in class, determine the size of the price bubble for 2016, 2017, 2018 and 2019.

(d) Using the same bubble model discussed, determine the market-expected probability that the bubble would NOT burst in 2017/2018 and 2018/2019?

Table E034 : Median monthly household income4 of economically active domestic households[2][3] by household size 1] Property Price (HKS per square meter) for Class A and Class B res 1 District Year 2001 2002 2003 Household Size Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 (HK$) 13,000 12.500 12.000 12,500 12.000 12.500 12.500 14.000 13,000 13,500 15,000 15,000 15,000 15,000 17,000 17.000 18,000 19,000 20,000 21 (HK$) 20,000 20,000 18.800 18,500 19,000 19,500 20,000 20,400 19,700 20.0001 21,000 22.000 23.000 24,000 25,000 25,300 27,000 28,300 28,900 (HK$) 18,600 18,000 16,700 17.100 17,500 18,000 19,000 20,000 19,200 20.000 21,000 23,000 24,900 26,000 27,500 29,500 30.000 32,700 33,500 4 (HK$) 21,000 20,000 19,500 19,700 20,000 21,200 22.100 23,500 23.300 24.4001 26.2001 29,400 31,400 33,000 35,800 37.400 40,000 42.800 43,500 51 (HK$) 25,9001 25,000 23,700 24.300 25,300 27,000 29,000 30,000 30,000 31,000 33,800 37,000 40,400 43,000 45,200 48,000 52.600 53,600 57,000 6 and Over (HK$) 30.2001 28.000 27,300 28,800 29,300 29,900 31,000 33,300 33,600 34,600 38.900 43,000 44,800 46.900 49,800 52,100 55,900 57.100 59,900 Overall (HK$) 20,100 20.000 18.800 19.0001 19,4001 20,000 20,500 21,600 21,000 21,800 23,500 25.200 27,000 28,500 30,000 31,200 32,700 35,000 35,500 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Kowloon A: 40 sqm or less 26 560 23 324 20 867 25 233 29 896 30 068 36 806 42 952 44 190 55 661 67 594 79 928 94 808 104 403 117 955 112 486 130 558 149 890 157 317 Kowloon B: 40-70 sqm 28 317 24 722 22 020 33 058 38 868 38 090 47 791 53 543 55 338 69 728 81 941 92 997 103 401 108 820 120 994 115 792 131 061 147 161 153 582 Notes: [1] [2] [3] Figures are rounded to the nearest hundred. Household size refers to the number of household members in a domestic household. Economically active household is a domestic household with at least one member (excluding foreign domestic helpers) being economically active. Domestic household consists of a group of persons who live together and make common provision for essentials for living. These persons need not be related. If a person makes provision for essentials for living without sharing with other persons, he/she is also regarded as a household. In this case, the household is a one-person household. Households comprising only non-Hong Kong residents or Mobile Residents are not classified as domestic households. Monthly household income refers to the total cash income (including earnings from all jobs and other cash income) received in the month before enumeration by all members of the household. Other cash income includes income generated from rent income, interest, dividends, regular/monthly pensions and insurance annuity benefits, regular contribution from persons outside the household, regular contribution from charities and all government subsidies. [4] Source: General Household Survey, Census and Statistics Department Table E034 : Median monthly household income4 of economically active domestic households[2][3] by household size 1] Property Price (HKS per square meter) for Class A and Class B res 1 District Year 2001 2002 2003 Household Size Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 (HK$) 13,000 12.500 12.000 12,500 12.000 12.500 12.500 14.000 13,000 13,500 15,000 15,000 15,000 15,000 17,000 17.000 18,000 19,000 20,000 21 (HK$) 20,000 20,000 18.800 18,500 19,000 19,500 20,000 20,400 19,700 20.0001 21,000 22.000 23.000 24,000 25,000 25,300 27,000 28,300 28,900 (HK$) 18,600 18,000 16,700 17.100 17,500 18,000 19,000 20,000 19,200 20.000 21,000 23,000 24,900 26,000 27,500 29,500 30.000 32,700 33,500 4 (HK$) 21,000 20,000 19,500 19,700 20,000 21,200 22.100 23,500 23.300 24.4001 26.2001 29,400 31,400 33,000 35,800 37.400 40,000 42.800 43,500 51 (HK$) 25,9001 25,000 23,700 24.300 25,300 27,000 29,000 30,000 30,000 31,000 33,800 37,000 40,400 43,000 45,200 48,000 52.600 53,600 57,000 6 and Over (HK$) 30.2001 28.000 27,300 28,800 29,300 29,900 31,000 33,300 33,600 34,600 38.900 43,000 44,800 46.900 49,800 52,100 55,900 57.100 59,900 Overall (HK$) 20,100 20.000 18.800 19.0001 19,4001 20,000 20,500 21,600 21,000 21,800 23,500 25.200 27,000 28,500 30,000 31,200 32,700 35,000 35,500 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Kowloon A: 40 sqm or less 26 560 23 324 20 867 25 233 29 896 30 068 36 806 42 952 44 190 55 661 67 594 79 928 94 808 104 403 117 955 112 486 130 558 149 890 157 317 Kowloon B: 40-70 sqm 28 317 24 722 22 020 33 058 38 868 38 090 47 791 53 543 55 338 69 728 81 941 92 997 103 401 108 820 120 994 115 792 131 061 147 161 153 582 Notes: [1] [2] [3] Figures are rounded to the nearest hundred. Household size refers to the number of household members in a domestic household. Economically active household is a domestic household with at least one member (excluding foreign domestic helpers) being economically active. Domestic household consists of a group of persons who live together and make common provision for essentials for living. These persons need not be related. If a person makes provision for essentials for living without sharing with other persons, he/she is also regarded as a household. In this case, the household is a one-person household. Households comprising only non-Hong Kong residents or Mobile Residents are not classified as domestic households. Monthly household income refers to the total cash income (including earnings from all jobs and other cash income) received in the month before enumeration by all members of the household. Other cash income includes income generated from rent income, interest, dividends, regular/monthly pensions and insurance annuity benefits, regular contribution from persons outside the household, regular contribution from charities and all government subsidies. [4] Source: General Household Survey, Census and Statistics Department