CHP 24

Question 1

Valuation of asset classes and portfolios

Answer 1

Relative value of different asset classes can be analysed by looking at the relationship between expected and required returns.
Total return is from income and capital gain:
Expected return = initial income yield + expected capital growth
Nominal return required is:
Required return = risk free yield + expected inflation + risk premium
Compare expected and required return to find out if the asset is relatively cheap or dear.
If there is a market in index-linked government bonds, the required risk free yield can be taken as the real yield on these.

Question 2

Valuation of asset classes and portfolios

Simplifying assumptions:

Answer 2

• All investors want a real rate of return
• All investors have the same time horizon for investment decisions
• Tax differences between investors can be ignored
• Reinvestment can occur at a rate equal to the expected total return on the asset.
In reality, these assumptions are questionable.
For each main asset category, the expected return from a portfolio of assets will be equated with the required return from that asset category. The equations considered are valid if the assets are fair value relative to each other.

Question 3

1.4. Conventional government bonds returns

Answer 3

Expected return = gross redemption yield

GRY = required risk-free real yield + expected inflation + inflation risk premium

Question 4

1.5. Corporate loan stocks returns

Answer 4

GRY = required risk-free yield + expected inflation + bond risk premium
Investors require a higher yield than from government bonds due to the higher risk of default and lower marketability. The bond risk has 3 components:
• Inflation risk premium
• Default premium
• Marketability premium

Question 5

1.6. Equities

Total expected return from equities

Answer 5

• d = income stream – i.e. dividend yield
• g = expected capital gain – i.e. annual growth in dividends (expected inflation + real div growth)
d + g = required risk free yield + expected inflation + equity risk premium
Equity risk premium is needed to compensate the investor for:
• possible default
• marketability
• high volatility of share prices and dividend income

Question 6

1.7. Property returns

Answer 6

Rental yield + expected growth in rents = required risk-free real yield + expected inflation + property risk premium

Question 7

1.8. Two reminders on expected vs required return

Answer 7

• Equalities above only apply where the assets are correctly priced. To see if an asset is cheap or not, prove the equality does not hold.
• The same results can be developed using nominal yields on long term government bonds instead of real yields.

Question 8

reverse yield gap

Answer 8

Yield gap = equity gross dividend yield – gross redemption yield on long-dated benchmark bond
Prior to the late 50’s, the yield gap was generally positive. Since then, this has become negative and hence the “reverse” yield gap emerged.
Reverse yield gap = gross redemption yield – gross dividend yield
Reverse yield gap can be split up into its components:
GRY – d = inflation risk premium (IRP) – equity risk premium (ERP) + g
Because g can be split up between expected inflation + expected real dividend growth:
Reverse yield gap = IRP – ERP + expected inflation + expected real dividend growth

Question 9

2.3. Property versus other sectors

Answer 9

Traditionally rental yields from property have been compared to dividend yields from equity – the reason is that both rent and dividends should increase in the long term.
The gap between rental yields and div yields:
Rental yield – div yield = property risk premium – equity risk premium + expected div growth – expected rental growth

If expectations for property rental growth are generally not high, it’s more appropriate to compare it to GRY’s from conventional bonds. (because rent will be more like fixed income rather than a growing income stream).
Rental yield – GRY = Property risk premium – inflation risk premium – expected rental growth.

Question 10

To justify property yields being above government bonds, at least one of the following must hold:

Answer 10

• Low expected future inflation
• Very low prospects for real rental growth
• Justifiably high risk premium for properties
If none of these hold, property yields are above gov bond yields, then property appears cheap relative to conventional gov bonds.

Question 11

2.4. Currency factors returns

Answer 11

To maximize returns in the domestic currency, also allow for the expected changes in the currencies over the period of the investment.
Overseas market will be considered cheap if:
Expected return in local currency + Expected depreciation of home currency > Expected return in home currency
Invest in overseas markets if the left hand side exceeds the right hand by more than the risk premium.

Question 12

3.1. Yield “norms”

Answer 12

For some of the asset categories there may be a normal level or range.
Care must be taken that there haven’t been fundamental shifts that brought the change in the “normal” range.

Question 13

3.2. Index levels and price charts

Answer 13

Technical analysis is sometimes used to compare the value of asset groupings as well as individual assets.

Question 14

3.3. Yield ratios

Answer 14

The yield ratio is sometimes used when assessing the relative price of equities and bonds.
Ratio = (GRY on benchmark gov bond) / (Gross div yield on benchmark equity index)
If the previous analysis is accepted, it will be seen that the ration has to be used with care as an indicator of relative value.

Question 15

4. Relationship between the assets and liabilities

4. 1. Consistency of valuation

Answer 15

The method and basis for any actuarial valuation will depend on the purpose of the valuation and the type of liability.
For some supervisory valuations, the actuarial method and basis will be set out in regulations.
In other cases, the actuary will have freedom to choose the method and basis (within limits of professional guidance).
It is important that the valuations of assets and liabilities are consistent.

Question 16

4. Relationship between the assets and liabilities

4. 2. Consistency of method

Answer 16

• Discontinuance valuation

* Ongoing valuation

Question 17

4. Relationship between the assets and liabilities

4. 3. Consistency of bases

Answer 17

Interest rate
This means that if assets are valued at the market value, liabilities should be valued at appropriate market based discount rates.

Alternatively, both assets and liabilities can be valued using the same interest rate – this will normally represent the long-term expected return on the assets held to back the liabilities.

In practice, two methods exist:
• Use an average rate to discount
• Hypothecate certain assets to cover certain liabilities – discount each block of A&L separately.

Question 18

Any market value implies an expected rate of return linked to the risk of the asset.

Answer 18

Thus it can be argued that the use of a single discount rate is inappropriate. Different discount rates should be used depending on the risks within the assets and liabilities to be valued. Could also consider other factors (marketability and term)
Since few liabilities are marketable, the discount rate based on the assets that best match them should be used.
Whether this is useful or not in practice to adopt such an approach will depend on the purpose of the valuation.

Question 19

5. Allowing for variability of asset prices

There are 2 sorts of variability to consider:

Answer 19

• An asset valuation result may be very volatile over a short period of time due to market movements (e.g. if market value is used)
• An asset valuation may be changed due to a change in the investment portfolio (e.g. major switch from gov bonds to equities may significantly alter a value based on discounted income flows).
These 2 aspects may be described as:
• Stability over time
• Influence of short-term investment decisions over the value of assets
Volatility of asset value is often stated as the main problem with a market value of assets. However, it can be argued that stability is not a desirable feature of asset valuation, and that consistency overrides stability.

Question 20

Volatility itself is not the problem in itself, a volatile valuation may correctly reflect the underlying reality.

Answer 20

However, in the context of ongoing valuation of a long-term fund, comparing volatile asset values with liabilities calculated using a stable interest rate could be misleading.

I.e. the problem with a market valuation of assets is not the volatility but rather the inconsistency with liability valuation basis.
In practice stability is sometimes a desirable feature. An unstable value of assets may be difficult to communicate and interpret. In addition to this, in practice it may not be easy to ensure that the liability valuation result is really consistent with an unstable value of assets.
One possibility is to modify the valuation method of the assets to make it more stable and thus more consistent with liabilities calculated using stable assumptions. Some sort of smoothed market valuation is sometimes seen as the solution to this problem.
Problem with this: if smoothed rate is used for assets, what is a consistent rate for liabilities?
More common method: use a discounted cashflow method, using a long-term interest rate assumption which is held relatively constant.

Question 21

6. Notional portfolios

6. 1. Method

Answer 21

Basing the split of assets on a notional portfolio overcomes 2 problems:
• The discounted income approach will produce a different ratio of the market value to calculated value for each asset in the actuarial valuation. The result of the valuation will be influenced by the actual investments held at the valuation date. However the actual distribution of assets represents the manager’s view on short- and long-term prospects of each asset class. The investments are likely to be replaced due to a change in that view.
• Replacing actual portfolio with a notional portfolio eliminates the risk that the valuation process is in conflict with the best investment policy of the fund. I.e. the investment decisions are made with the valuation result being the prime conclusion rather than the investment reasons.

Question 22

6. Notional portfolios

6. 1. Method simplified

Answer 22

• Results of the valuation are influenced by the actual assets held on the valuation date, which could represent short-term tactical switches rather than long-term investment strategy.
• Investment strategy can be influenced by the results of the valuation.

Question 23

Using notional portfolios:

Answer 23

• Removes the problem of having to estimate future cashflows on each asset
• Reduces the amount of calculation required.

Question 24

6.2. Choosing the notional portfolio

Answer 24

A notional portfolio can be based on the long-term strategic investment benchmark.
A notional fund is a tool to smooth the results of an actuarial valuation over time. It is not to establish a benchmark for strategic asset allocation.
Therefore a more pragmatic approach is normally used – the notional fund will reflect the broad characteristics of the liability profile. It will also be influenced by not wanting to change the actuarial basis unnecessarily. The notional portfolio may also pay some regard to the current investment strategy.