How large is it?

Very large.
Total assets under management (AUM) in Japanese financial markets are estimated at JPY 1,970 trillion (as of March 2017, Nomura Research Institute).
The Toshin Kyokai (Investments Trusts Association, Japan – JITA) counts 102 asset management (AM) companies as members, including many non-domestic AM companies and excluding REIT firms (as of July 2018). A number of unlicensed non-Japanese AM companies market in Japan via partnerships with licensed AM companies.

Who are the major investors in Japan?

Various institutional investors and individual investors.
Institutional investors: pension funds, banks, insurance companies, etc.

i）Pension funds（Nenkin） Over JPY 300 trillion in total

Government Pension Investment Fund (GPIF)
 JPY 156 trillion (as of March 2018, GPIF)
Corporate pensions (Defined Benefit Pension Plan)
 JPY 59 trillion (as of March 2017, Ministry of Health, Labor and Welfare (MHLW))

ii）Commercial banks

Most Japanese banks house proprietary trading division (Shikin Unyo Bu); however, aside from those at the Big Three (megabanks: Mitsubishi UFJ, Sumitomo Mitsui and Mizuho) and Japan Post Bank (Yucho Ginko), asset management divisions are poorly staffed as their primary role traditionally has been to buy and sell Japanese Government Bond (JGB).
Under Japan's regime of very low interest rates, banks, especially regional banks (chiho ginko, shinyo kinko), have diversified portfolios through outsourcing. AM companies provide a variety of funds (private placement) to the regional banks.

iii）Insurance companies

The AUM among members of Life Insurance Association is JPY 313 trillion (as of March 2018). The AUM of General Insurance Association of Japan members is JPY 24 trillion (as of June 2018).
Major insurance companies also operate as AM companies for pension funds and other institutional investors.

Individual investors

For many years, Japanese individuals have preferred bank savings to investment to investment. However, the volume of investments by individuals has been slowly increasing of late.
Some individuals still tend to prefer selecting individual stocks or Forex trading, but more and more are making long-term investment via Toshin funds (Japanese version of mutual funds), including ETFs.
 Toshin funds JPY 113 trillion (as of July 2018, JITA).

What asset classes are popular among the Japanese investors?

In the past, pension fund and insurance company portfolios were comprised primarily of Japanese Government Bond (JGB). However, due to the very low interest rates maintained by Bank of Japan (BOJ) policy (near 0% for 10-year JGBs since 2016), holding JGBs no longer works.
As a result, Japanese institutional investors have diversified their portfolios, with allocations trending toward more domestic and foreign stocks and foreign bonds.
Banks prefer listed securities, such as REITs and ETFs.
Pension funds tend to choose private-placement funds as alternative assets, including hedge fund, real estate, private equity, and infrastructure-related securities.